Nicolas Markey

@inproceedings{stoc1985-Bab,
  author =              {Babai, L{\'a}szl{\'o}},
  title =               {Trading Group Theory for Randomness},
  booktitle =           {{P}roceedings of the 17th {A}nnual {ACM} {S}ymposium
                         on the {T}heory of {C}omputing ({STOC}'85)},
  acronym =             {{STOC}'85},
  publisher =           {ACM Press},
  pages =               {421-429},
  year =                {1985},
  month =               may,
}

@inproceedings{fmics2002-BAS,
  author =              {Biere, Armin and Artho, Cyrille and Schuppan,
                         Viktor},
  title =               {Liveness Checking as Safety Checking},
  editor =              {Cleaveland, Rance and Garavel, Hubert},
  booktitle =           {{P}roceedings of the 7th {I}nternational {ERCIM}
                         {W}orkshop in {F}ormal {M}ethods for {I}ndustrial
                         {C}ritical {S}ystems ({FMICS}'02)},
  acronym =             {{FMICS}'02},
  publisher =           {Elsevier},
  series =              {Electronic Notes in Theoretical Computer Science},
  volume =              {66},
  number =              {2},
  year =                {2002},
  month =               jul,
}

@article{fac3(2)-BB,
  author =              {Baeten, Jos C. M. and Bergstra, Jan A.},
  title =               {Real Time Process Algebra},
  publisher =           {Springer-Verlag},
  journal =             {Formal Aspects of Computing},
  volume =              {3},
  number =              {2},
  pages =               {142-188},
  year =                {1991},
}

@incollection{lncs2500-BB,
  author =              {Berwanger, Dietmar and Blumensath, Achim},
  title =               {The Monadic Theory of Tree-like Structures},
  editor =              {Gr{\"a}del, Erich and Thomas, Wolfgang and Wilke,
                         Thomas},
  booktitle =           {Automata, Logics, and Infinite Games},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2500},
  pages =               {285-302},
  chapter =             {16},
  year =                {2002},
}

@inproceedings{BB-fates2004,
  author =              {Briones, Laura Brand{\'a}n and Brinksma, Ed},
  title =               {A~Test Generation Framework for Quiescent Real-Time
                         Systems},
  editor =              {Grabowski, Jens and Nielsen, Brian},
  booktitle =           {{P}roceedings of the 4th {I}nternational {W}orkshop
                         on {F}ormal {A}pproaches to {S}oftware {T}esting
                         ({FATES}'04)},
  acronym =             {{FATES}'04},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {3395},
  pages =               {64-78},
  year =                {2004},
  month =               sep,
  doi =                 {10.1007/978-3-540-31848-4_5},
}

@inproceedings{icalp2009-BBBB,
  author =              {Baier, {\relax Ch}ristel and Bertrand, Nathalie and
                         Bouyer, Patricia and Brihaye, {\relax Th}omas},
  title =               {When are timed automata determinizable?},
  editor =              {Albers, Susanne and Marchetti{-}Spaccamela Alberto
                         and Matias, Yossi and Nikoletseas, Sotiris and
                         Thomas, Wolfgang},
  booktitle =           {{P}roceedings of the 36th {I}nternational
                         {C}olloquium on {A}utomata, {L}anguages and
                         {P}rogramming ({ICALP}'09)~-- Part~{II}},
  acronym =             {{ICALP}'09},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {5556},
  pages =               {43-54},
  year =                {2009},
  month =               jul,
  doi =                 {10.1007/978-3-642-02930-1_4},
}

@inproceedings{fsttcs2007-BBBBG,
  author =              {Baier, {\relax Ch}ristel and Bertrand, Nathalie and
                         Bouyer, Patricia and Brihaye, {\relax Th}omas and
                         Gr{\"o}{\ss}er, Marcus},
  title =               {Probabilistic and Topological Semantics for Timed
                         Automata},
  editor =              {Arvind, Vikraman and Prasad, Sanjiva},
  booktitle =           {{P}roceedings of the 27th {C}onference on
                         {F}oundations of {S}oftware {T}echnology and
                         {T}heoretical {C}omputer {S}cience ({FSTTCS}'07)},
  acronym =             {{FSTTCS}'07},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {4855},
  pages =               {179-191},
  year =                {2007},
  month =               dec,
}

@inproceedings{lics2008-BBBBG,
  author =              {Baier, {\relax Ch}ristel and Bertrand, Nathalie and
                         Bouyer, Patricia and Brihaye, {\relax Th}omas and
                         Gr{\"o}{\ss}er, Marcus},
  title =               {Almost-sure Model Checking of Infinite Paths in
                         One-clock Timed Automata},
  booktitle =           {{P}roceedings of the 23rd {A}nnual {S}ymposium on
                         {L}ogic in {C}omputer {S}cience ({LICS}'08)},
  acronym =             {{LICS}'08},
  publisher =           {IEEE Comp. Soc. Press},
  pages =               {217-226},
  year =                {2008},
  month =               jun,
  doi =                 {10.1109/LICS.2008.25},
}

@article{deds17(4)-BBBCD,
  author =              {Badouel, {\'E}ric and Bednarczyk, Marek and
                         Borzyszkowski, Andrzej and Caillaud, Beno{\^\i}t and
                         Darondeau, Philippe},
  title =               {Concurrent secrets},
  publisher =           {Kluwer Academic},
  journal =             {Discrete Event Dynamic Systems},
  volume =              {17},
  number =              {4},
  pages =               {425-446},
  year =                {2007},
  month =               dec,
  doi =                 {10.1007/s10626-007-0020-5},
}

Abstract

In [Baier et al., Probabilistic and Topological Semantics for Timed Automata, FSTTCS'07] a probabilistic semantics for timed automata has been defined in order to rule out unlikely (sequences of) events. The qualitative model-checking problem for LTL properties has been investigated, where the aim is to check whether a given LTL property holds with probability 1 in a timed automaton, and solved for the class of single-clock timed automata.

In this paper, we consider the quantitative model-checking problem for ω-regular properties: we aim at computing the exact probability that a given timed automaton satisfies an ω-regular property. We develop a framework in which we can compute a closed-form expression for this probability; we furthermore give an approximation algorithm, and finally prove that we can decide the threshold problem in that framework.

@inproceedings{qest2008-BBBM,
  author =              {Bertrand, Nathalie and Bouyer, Patricia and Brihaye,
                         {\relax Th}omas and Markey, Nicolas},
  title =               {Quantitative Model-Checking of One-Clock Timed
                         Automata under Probabilistic Semantics},
  booktitle =           {{P}roceedings of the 5th {I}nternational
                         {C}onference on {Q}uantitative {E}valuation of
                         {S}ystems ({QEST}'08)},
  acronym =             {{QEST}'08},
  publisher =           {IEEE Comp. Soc. Press},
  pages =               {55-64},
  year =                {2008},
  month =               sep,
  doi =                 {10.1109/QEST.2008.19},
  abstract =            {In [Baier \emph{et~al.}, \textit{Probabilistic and
                         Topological Semantics for Timed Automata},
                         FSTTCS'07] a probabilistic semantics for timed
                         automata has been defined in order to rule out
                         unlikely (sequences of) events. The qualitative
                         model-checking problem for LTL properties has been
                         investigated, where the aim is to check whether a
                         given LTL property holds with probability~\(1\) in a
                         timed automaton, and solved for the class of
                         single-clock timed automata.\par In this paper, we
                         consider the quantitative model-checking problem for
                         \(\omega\)-regular properties: we aim at computing
                         the exact probability that a given timed automaton
                         satisfies an \(\omega\)-regular property. We develop
                         a framework in which we can compute a closed-form
                         expression for this probability; we furthermore give
                         an approximation algorithm, and finally prove that
                         we can decide the threshold problem in that
                         framework.},
}

@article{lmcs10(4)-BBBMBGJ,
  author =              {Bertrand, Nathalie and Bouyer, Patricia and Brihaye,
                         {\relax Th}omas and Menet, Quentin and Baier,
                         {\relax Ch}ristel and Gr{\"o}{\ss}er, Marcus and
                         Jurdzi{\'n}ski, Marcin},
  title =               {Stochastic Timed Automata},
  journal =             {Logical Methods in Computer Science},
  volume =              {10},
  number =              {4},
  year =                {2014},
  month =               dec,
  doi =                 {10.2168/LMCS-10(4:6)2014},
}

@article{fmsd31(2)-BBBR,
  author =              {Bouyer, Patricia and Brihaye, {\relax Th}omas and
                         Bruy{\`e}re, V{\'e}ronique and Raskin, Jean-Fran{\c
                         c}ois},
  title =               {On the Optimal Reachability Problem of Weighted
                         Timed Automata},
  publisher =           {Springer-Verlag},
  journal =             {Formal Methods in System Design},
  volume =              {31},
  number =              {2},
  pages =               {135-175},
  year =                {2007},
  month =               oct,
  doi =                 {10.1007/s10703-007-0035-4},
}

@book{BBC92,
  author =              {Beauquier, Dani{\`e}le and Berstel, Jean and
                         Chr{\'e}tienne, {\relax Ph}ilippe},
  title =               {{\'E}l{\'e}ments d'algorithmique},
  publisher =           {Masson},
  year =                {1992},
}

@inproceedings{emsoft2010-BBC,
  author =              {Benveniste, Albert and Bouillard, Anne and Caspi,
                         Paul},
  title =               {A~unifying view of loosely time-triggered
                         architectures},
  editor =              {Carloni, Luca P. and Tripakis, Stavros},
  booktitle =           {{P}roceedings of the 10th {I}nternational
                         {C}onference on {E}mbedded {S}oftware ({EMSOFT}'10)},
  acronym =             {{EMSOFT}'10},
  publisher =           {ACM Press},
  pages =               {189-198},
  year =                {2010},
  month =               oct,
  doi =                 {10.1145/1879021.1879047},
}

@article{tcsyst54(2)-BBD,
  author =              {Brihaye, {\relax Th}omas and Bruy{\`e}re,
                         V{\'e}ronique and De{~}Pril, Julie},
  title =               {On Equilibria in Quantitative Games with
                         Reachability{{\slash}}Safety Objectives},
  publisher =           {Springer-Verlag},
  journal =             {Theory of Computing Systems},
  volume =              {54},
  number =              {2},
  pages =               {150-189},
  year =                {2014},
  month =               feb,
}

@inproceedings{atva2011-BBDDR,
  author =              {Brihaye, {\relax Th}omas and Bruy{\`e}re,
                         V{\'e}ronique and Doyen, Laurent and Ducobu, Marc
                         and Raskin, Jean-Fran{\c c}ois},
  title =               {Antichain-based {QBF} Solving},
  editor =              {Bultan, Tevfik and Hsiung, Pao-Ann},
  booktitle =           {{P}roceedings of the 9th {I}nternational {S}ymposium
                         on {A}utomated {T}echnology for {V}erification and
                         {A}nalysis ({ATVA}'11)},
  acronym =             {{ATVA}'11},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {6996},
  pages =               {183-197},
  year =                {2011},
  month =               oct,
}

@inproceedings{fossacs2012-BBDG,
  author =              {Brihaye, {\relax Th}omas and Bruy{\`e}re,
                         V{\'e}ronique and De{~}Pril, Julie and Gimbert,
                         Hugo},
  title =               {Subgame Perfection for Equilibria in Quantitative
                         Reachability Games},
  editor =              {Birkedal, Lars},
  booktitle =           {{P}roceedings of the 15th {I}nternational
                         {C}onference on {F}oundations of {S}oftware
                         {S}cience and {C}omputation {S}tructure
                         ({FoSSaCS}'12)},
  acronym =             {{FoSSaCS}'12},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {7213},
  pages =               {286-300},
  year =                {2012},
  month =               mar,
}

@inproceedings{ftrtft2002-BBDLPY,
  author =              {Behrmann, Gerd and Bengtsson, Johan and David,
                         Alexandre and Larsen, Kim Guldstrand and Pettersson,
                         Paul and Yi, Wang},
  title =               {UPPAAL Implementation Secrets},
  editor =              {Damm, Werner and Olderog, Ernst R{\"u}diger},
  booktitle =           {{P}roceedings of the 7th {F}ormal {T}echniques in
                         {R}eal-Time and {F}ault-Tolerant {S}ystems
                         ({FTRTFT}'02)},
  acronym =             {{FTRTFT}'02},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2469},
  pages =               {3-22},
  year =                {2002},
  month =               sep,
  doi =                 {10.1007/3-540-45739-9_1},
}

@inproceedings{lics2006-BBFK,
  author =              {Br{\'a}zdil, Tom{\'a}{\v s} and V{\'a}clav
                         Bro{\v{z}}ek and Forejt, Vojt{\v{e}}ch and Ku{\v
                         c}era, Anton{\'\i}n},
  title =               {Stochastic Games with Branching-Time Winning
                         Objectives},
  booktitle =           {{P}roceedings of the 21st {A}nnual {S}ymposium on
                         {L}ogic in {C}omputer {S}cience ({LICS}'06)},
  acronym =             {{LICS}'06},
  publisher =           {IEEE Comp. Soc. Press},
  pages =               {349-358},
  year =                {2006},
  month =               jul,
}

@inproceedings{tacas2003-BBFL,
  author =              {Behrmann, Gerd and Bouyer, Patricia and Fleury,
                         Emmanuel and Larsen, Kim Guldstrand},
  title =               {Static Guard Analysis in Timed Automata
                         Verification},
  editor =              {Garavel, Hubert and Hatcliff, John},
  booktitle =           {{P}roceedings of the 9th {I}nternational
                         {C}onference on {T}ools and {A}lgorithms for
                         {C}onstruction and {A}nalysis of {S}ystems
                         ({TACAS}'03)},
  acronym =             {{TACAS}'03},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2619},
  pages =               {254-270},
  year =                {2003},
  month =               apr,
}

Abstract

In this paper, we propose a novel framework for the synthesis of robust and optimal energy-aware controllers. The framework is based on energy timed automata, allowing for easy expression of timing-constraints and variable energy-rates. We prove decidability of the energy-constrained infinite-run problem in settings with both certainty and uncertainty of the energy-rates. We also consider the optimization problem of identifying the minimal upper bound that will permit existence of energy-constrained infinite runs. Our algorithms are based on quantifier elimination for linear real arithmetic. Using Mathematica and Mjollnir, we illustrate our framework through a real industrial example of a hydraulic oil pump. Compared with previous approaches our method is completely automated and provides improved results.

@inproceedings{fm2018-BBFLMR,
  author =              {Bacci, Giovanni and Bouyer, Patricia and Fahrenberg,
                         Uli and Larsen, Kim Guldstrand and Markey, Nicolas
                         and Reynier, Pierre-Alain},
  title =               {Optimal and Robust Controller Synthesis Using Energy
                         Timed Automata with Uncertainty},
  editor =              {Havelund, Klaus and Peleska, Jan and Roscoe, Bill W.
                         and de Vink, Erik},
  booktitle =           {{P}roceedings of the 22nd {I}nternational
                         {S}ymposium on {F}ormal {M}ethods ({FM}'18)},
  acronym =             {{FM}'18},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {10951},
  pages =               {203-221},
  year =                {2018},
  month =               jul,
  doi =                 {10.1007/978-3-319-95582-7_12},
  abstract =            {In this paper, we propose a novel framework for the
                         synthesis of robust and optimal energy-aware
                         controllers. The framework is based on energy timed
                         automata, allowing for easy expression of
                         timing-constraints and variable energy-rates. We
                         prove decidability of the energy-constrained
                         infinite-run problem in settings with both certainty
                         and uncertainty of the energy-rates. We also
                         consider the optimization problem of identifying the
                         minimal upper bound that will permit existence of
                         energy-constrained infinite runs. Our algorithms are
                         based on quantifier elimination for linear real
                         arithmetic. Using Mathematica and Mjollnir, we
                         illustrate our framework through a real industrial
                         example of a hydraulic oil pump. Compared with
                         previous approaches our method is completely
                         automated and provides improved results.},
}

Abstract

In this paper, we propose a novel framework for the synthesis of robust and optimal energy-aware controllers. The framework is based on energy timed automata, allowing for easy expression of timing-constraints and variable energy-rates. We prove decidability of the energy-constrained infinite-run problem in settings with both certainty and uncertainty of the energy-rates. We also consider the optimization problem of identifying the minimal upper bound that will permit existence of energy-constrained infinite runs. Our algorithms are based on quantifier elimination for linear real arithmetic. Using Mathematica and Mjollnir, we illustrate our framework through a real industrial example of a hydraulic oil pump. Compared with previous approaches our method is completely automated and provides improved results.

@article{fac2020-BBFLMR,
  author =              {Bacci, Giovanni and Bouyer, Patricia and Fahrenberg,
                         Uli and Larsen, Kim Guldstrand and Markey, Nicolas
                         and Reynier, Pierre-Alain},
  title =               {Optimal and Robust Controller Synthesis Using Energy
                         Timed Automata with Uncertainty},
  publisher =           {Springer-Verlag},
  journal =             {Formal Aspects of Computing},
  volume =              {33},
  number =              {1},
  pages =               {3-25},
  year =                {2021},
  month =               jan,
  doi =                 {10.1007/s00165-020-00521-4},
  abstract =            {In~this paper, we~propose a novel framework for the
                         synthesis of robust and optimal energy-aware
                         controllers. The~framework is based on energy timed
                         automata, allowing for easy expression of
                         timing-constraints and variable energy-rates.
                         We~prove decidability of the energy-constrained
                         infinite-run problem in settings with both certainty
                         and uncertainty of the energy-rates. We~also
                         consider the optimization problem of identifying the
                         minimal upper bound that will permit existence of
                         energy-constrained infinite runs. Our~algorithms are
                         based on quantifier elimination for linear real
                         arithmetic. Using Mathematica and Mjollnir,
                         we~illustrate our framework through a real
                         industrial example of a hydraulic oil pump. Compared
                         with previous approaches our method is completely
                         automated and provides improved results.},
}

@book{SSV2001-BBFLPPS,
  author =              {B{\'e}rard, B{\'e}atrice and Bidoit, Michel and
                         Finkel, Alain and Laroussinie, Fran{\c c}ois and
                         Petit, Antoine and Petrucci, Laure and Schnoebelen,
                         {\relax Ph}ilippe and McKenzie, Pierre},
  title =               {Systems and Software Verification: Model-Checking
                         Techniques and Tools},
  publisher =           {Springer-Verlag},
  year =                {2001},
}

@inproceedings{tacas2013-BBFR,
  author =              {Bohy, Aaron and Bruy{\`e}re, V{\'e}ronique and
                         Filiot, Emmanuel and Raskin, Jean-Fran{\c c}ois},
  title =               {Synthesis from {LTL} Specifications with Mean-Payoff
                         Objectives},
  editor =              {Piterman, Nir and Smolka, Scott A.},
  booktitle =           {{P}roceedings of the 19th {I}nternational
                         {C}onference on {T}ools and {A}lgorithms for
                         {C}onstruction and {A}nalysis of {S}ystems
                         ({TACAS}'13)},
  acronym =             {{TACAS}'13},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {7795},
  pages =               {169-184},
  year =                {2013},
  month =               mar,
}

@inproceedings{qest2007-BBGK,
  author =              {Baier, {\relax Ch}ristel and Br{\'a}zdil,
                         Tom{\'a}{\v s} and Gr{\"o}{\ss}er, Marcus and Ku{\v
                         c}era, Anton{\'\i}n},
  title =               {Stochastic Game Logic},
  booktitle =           {{P}roceedings of the 4th {I}nternational
                         {C}onference on {Q}uantitative {E}valuation of
                         {S}ystems ({QEST}'07)},
  acronym =             {{QEST}'07},
  publisher =           {IEEE Comp. Soc. Press},
  pages =               {227-236},
  year =                {2007},
  month =               sep,
}

@article{acta49(4)-BBGK,
  author =              {Baier, {\relax Ch}ristel and Br{\'a}zdil,
                         Tom{\'a}{\v s} and Gr{\"o}{\ss}er, Marcus and Ku{\v
                         c}era, Anton{\'\i}n},
  title =               {Stochastic Game Logic},
  publisher =           {Springer-Verlag},
  journal =             {Acta Informatica},
  volume =              {49},
  number =              {4},
  pages =               {203-224},
  year =                {2012},
  month =               jun,
  doi =                 {10.1007/s00236-012-0156-0},
}

@inproceedings{concur2019-BBGRB,
  author =              {Brihaye, {\relax Th}omas and Bruy{\`e}re,
                         V{\'e}ronique and Goeminne, Aline and Raskin,
                         Jean-Fran{\c c}ois and Van{~}den{ }Bogaard, Marie},
  title =               {The~Complexity of Subgame Perfect Equilibria in
                         Quantitative Reachability Games},
  editor =              {Fokkink, Wan J. and van Glabbeek, Rob},
  booktitle =           {{P}roceedings of the 30th {I}nternational
                         {C}onference on {C}oncurrency {T}heory
                         ({CONCUR}'19)},
  acronym =             {{CONCUR}'19},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {140},
  pages =               {13:1-13:16},
  year =                {2019},
  month =               aug,
  doi =                 {10.4230/LIPIcs.CONCUR.2019.13},
}

@inproceedings{BBJKNN-isola2014,
  author =              {Bohlender, Dimitri and Bruintjes, Harold and Junges,
                         Sebastian and Katelaan, Jens and Nguyen, Viet Yen
                         and Noll, Thomas},
  title =               {A~Review of Statistical Model Checking Pitfalls on
                         Real-Time Stochastic Models},
  editor =              {Margaria, Tiziana and Steffen, Bernhard},
  booktitle =           {{P}roceedings of the 6th {I}nternational {S}ymposium
                         on {L}everaging {A}pplications of {F}ormal
                         {M}ethods, {V}erification and {V}alidation
                         ({IS}o{LA}'14)~-- {P}art~{II}: {S}pecialized
                         {T}echniques and {A}pplications},
  acronym =             {{IS}o{LA}'14},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {8803},
  pages =               {177-192},
  year =                {2014},
  month =               oct,
  doi =                 {10.1007/978-3-662-45231-8_13},
}

@inproceedings{hscc2004-BBL,
  author =              {Bouyer, Patricia and Brinksma, Ed and Larsen, Kim
                         Guldstrand},
  title =               {Staying Alive as Cheaply as Possible},
  editor =              {Alur, Rajeev and Pappas, George J.},
  booktitle =           {{P}roceedings of the 7th {I}nternational {W}orkshop
                         on {H}ybrid {S}ystems: {C}omputation and {C}ontrol
                         ({HSCC}'04)},
  acronym =             {{HSCC}'04},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2993},
  pages =               {203-218},
  year =                {2004},
  month =               mar,
}

@article{fmsd32(1)-BBL,
  author =              {Bouyer, Patricia and Brinksma, Ed and Larsen, Kim
                         Guldstrand},
  title =               {Optimal infinite scheduling for multi-priced timed
                         automata},
  publisher =           {Springer-Verlag},
  journal =             {Formal Methods in System Design},
  volume =              {32},
  number =              {1},
  pages =               {2-23},
  year =                {2008},
  month =               feb,
}

@inproceedings{mfcs2013-BBLM,
  author =              {Bacci, Giorgio and Bacci, Giovanni and Larsen, Kim
                         Guldstrand and Mardare, Radu},
  title =               {Computing Behavioral Distances, Compositionally},
  editor =              {Chatterjee, Krishnendu and Sgall, Ji{\v r}{\'\i}},
  booktitle =           {{P}roceedings of the 38th {I}nternational
                         {S}ymposium on {M}athematical {F}oundations of
                         {C}omputer {S}cience ({MFCS}'13)},
  acronym =             {{MFCS}'13},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {8087},
  pages =               {74-85},
  year =                {2013},
  month =               aug,
  doi =                 {10.1007/978-3-642-40313-2_9},
}

@inproceedings{qest2013-BBLM,
  author =              {Bacci, Giorgio and Bacci, Giovanni and Larsen, Kim
                         Guldstrand and Mardare, Radu},
  title =               {The BisimDist Library: Efficient Computation of
                         Bisimilarity Distances for {M}arkovian Models},
  booktitle =           {{P}roceedings of the 10th {I}nternational
                         {C}onference on {Q}uantitative {E}valuation of
                         {S}ystems ({QEST}'13)},
  acronym =             {{QEST}'13},
  publisher =           {IEEE Comp. Soc. Press},
  pages =               {278-281},
  year =                {2013},
  month =               aug,
  doi =                 {10.1007/978-3-642-40196-1_23},
}

@inproceedings{tacas2004-BBLP,
  author =              {Behrmann, Gerd and Bouyer, Patricia and Larsen, Kim
                         Guldstrand and Pel{\'a}nek, Radek},
  title =               {Lower and Upper Bounds in Zone-Based Abstractions of
                         Timed Automata},
  editor =              {Jensen, Kurt and Podelski, Andreas},
  booktitle =           {{P}roceedings of the 10th {I}nternational
                         {C}onference on {T}ools and {A}lgorithms for
                         {C}onstruction and {A}nalysis of {S}ystems
                         ({TACAS}'04)},
  acronym =             {{TACAS}'04},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2988},
  pages =               {312-326},
  year =                {2004},
  month =               mar,
  doi =                 {10.1007/978-3-540-24730-2_25},
}

@article{sttt8(3)-BBLP,
  author =              {Behrmann, Gerd and Bouyer, Patricia and Larsen, Kim
                         Guldstrand and Pel{\'a}nek, Radek},
  title =               {Lower and Upper Bounds in Zone-Based Abstractions of
                         Timed Automata},
  publisher =           {Springer-Verlag},
  journal =             {International Journal on Software Tools for
                         Technology Transfer},
  volume =              {8},
  number =              {3},
  pages =               {204-215},
  year =                {2006},
  month =               jun,
  doi =                 {10.1007/s10009-005-0190-0},
}

@inproceedings{icalp2015-BBLS,
  author =              {Bene{\v{s}}, Nikola and Bezdek, Petr and Larsen, Kim
                         Guldstrand and Srba, Ji{\v r}{\'\i}},
  title =               {Language Emptiness of Continuous-Time Parametric
                         Timed Automata},
  editor =              {Halld{\'o}rsson, Magn{\'u}s M. and Iwana, Kazuo and
                         Kobayashi, Naoki and Speckmann, Bettina},
  booktitle =           {{P}roceedings of the 42nd {I}nternational
                         {C}olloquium on {A}utomata, {L}anguages and
                         {P}rogramming ({ICALP}'15)~-- Part~{II}},
  acronym =             {{ICALP}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9135},
  pages =               {69-81},
  year =                {2015},
  month =               jul,
  doi =                 {10.1007/978-3-662-47666-6_6},
}

@inproceedings{concur2006-BBM,
  author =              {Ben{~}Salah, Ramzi and Bozga, Marius and Maler,
                         Oded},
  title =               {On Interleaving in Timed Automata},
  editor =              {Baier, {\relax Ch}ristel and Hermanns, Holger},
  booktitle =           {{P}roceedings of the 17th {I}nternational
                         {C}onference on {C}oncurrency {T}heory
                         ({CONCUR}'06)},
  acronym =             {{CONCUR}'06},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {4137},
  pages =               {465-476},
  year =                {2006},
  month =               aug,
}

Abstract

In this paper, we improve two recent undecidability results of Brihaye, Bruyère and Raskin about weighted timed automata, an extension of timed automata with a cost variable. Our results rely on a new encoding of the two counters of a Minsky machine that only require three clocks and one stopwatch cost, while previous reductions required five clocks and one stopwatch cost.

@article{ipl98(5)-BBM,
  author =              {Bouyer, Patricia and Brihaye, {\relax Th}omas and
                         Markey, Nicolas},
  title =               {Improved Undecidability Results on Weighted Timed
                         Automata},
  publisher =           {Elsevier},
  journal =             {Information Processing Letters},
  volume =              {98},
  number =              {5},
  pages =               {188-194},
  year =                {2006},
  month =               jun,
  doi =                 {10.1016/j.ipl.2006.01.012},
  abstract =            {In this paper, we improve two recent undecidability
                         results of Brihaye, Bruy{\`e}re and Raskin about
                         weighted timed automata, an extension of timed
                         automata with a cost variable. Our results rely on a
                         new encoding of the two counters of a Minsky machine
                         that only require three clocks and one stopwatch
                         cost, while previous reductions required five clocks
                         and one stopwatch cost.},
}

Abstract

We propose a procedure for computing Nash equilibria in multi-player timed games with reachability objectives. Our procedure is based on the construction of a finite concurrent game, and on a generic characterization of Nash equilibria in (possibly infinite) concurrent games. Along the way, we use our characterization to compute Nash equilibria in finite concurrent games.

@inproceedings{concur2010-BBM,
  author =              {Bouyer, Patricia and Brenguier, Romain and Markey,
                         Nicolas},
  title =               {{N}ash Equilibria for Reachability Objectives in
                         Multi-player Timed Games},
  editor =              {Gastin, Paul and Laroussinie, Fran{\c c}ois},
  booktitle =           {{P}roceedings of the 21st {I}nternational
                         {C}onference on {C}oncurrency {T}heory
                         ({CONCUR}'10)},
  acronym =             {{CONCUR}'10},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {6269},
  pages =               {192-206},
  year =                {2010},
  month =               sep,
  doi =                 {10.1007/978-3-642-15375-4_14},
  abstract =            {We propose a procedure for computing Nash equilibria
                         in multi-player timed games with reachability
                         objectives. Our procedure is based on the
                         construction of a finite concurrent game, and on a
                         generic characterization of Nash equilibria in
                         (possibly infinite) concurrent games. Along the way,
                         we~use our characterization to compute Nash
                         equilibria in finite concurrent games.},
}

Abstract

We study two-player timed games where the objectives of the two players are not opposite. We focus on the standard notion of Nash equilibrium and propose a series of transformations that builds two finite turn-based games out of a timed game, with a precise correspondence between Nash equilibria in the original and in final games. This provides us with an algorithm to compute Nash equilibria in two-player timed games for large classes of properties.

@inproceedings{formats2010-BBM,
  author =              {Bouyer, Patricia and Brenguier, Romain and Markey,
                         Nicolas},
  title =               {Computing Equilibria in Two-Player Timed Games
                         {\textit{via}}~Turn-Based Finite Games},
  editor =              {Chatterjee, Krishnendu and Henzinger, Thomas A.},
  booktitle =           {{P}roceedings of the 8th {I}nternational
                         {C}onferences on {F}ormal {M}odelling and {A}nalysis
                         of {T}imed {S}ystems ({FORMATS}'10)},
  acronym =             {{FORMATS}'10},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {6246},
  pages =               {62-76},
  year =                {2010},
  month =               sep,
  doi =                 {10.1007/978-3-642-15297-9_7},
  abstract =            {We study two-player timed games where the objectives
                         of the two players are not opposite. We focus on the
                         standard notion of Nash equilibrium and propose a
                         series of transformations that builds two finite
                         turn-based games out of a timed game, with a precise
                         correspondence between Nash equilibria in the
                         original and in final games. This provides us with
                         an algorithm to compute Nash equilibria in
                         two-player timed games for large classes of
                         properties.},
}

Abstract

Reconfigurable broadcast networks provide a convenient formalism for modelling and reasoning about networks of mobile agents broadcasting messages to other agents following some (evolving) communication topology. The parameterized verification of such models aims at checking whether a given property holds irrespective of the initial configuration (number of agents, initial states and initial communication topology). We focus here on the synchronization property, asking whether all agents converge to a set of target states after some execution. This problem is known to be decidable in polynomial time when no constraints are imposed on the evolution of the communication topology (while it is undecidable for static broadcast networks).

In this paper we investigate how various constraints on reconfigurations affect the decidability and complexity of the synchronization problem. In particular, we show that when bounding the number of reconfigured links between two communications steps by a constant, synchronization becomes undecidable; on the other hand, synchronization remains decidable in PTIME when the bound grows with the number of agents.

@inproceedings{tacas2018-2-BBM,
  author =              {Balasubramanian, A. R. and Bertrand, Nathalie and
                         Markey, Nicolas},
  title =               {Parameterized verification of synchronization in
                         constrained reconfigurable broadcast networks},
  editor =              {Beyer, Dirk and Huisman, Marieke},
  booktitle =           {{P}roceedings of the 24th {I}nternational
                         {C}onference on {T}ools and {A}lgorithms for
                         {C}onstruction and {A}nalysis of {S}ystems
                         ({TACAS}'18)~-- {P}art~{II}},
  acronym =             {{TACAS}'18 (Part~{II})},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {10806},
  pages =               {38-54},
  year =                {2018},
  month =               apr,
  doi =                 {10.1007/978-3-319-89963-3_3},
  abstract =            {Reconfigurable broadcast networks provide a
                         convenient formalism for modelling and reasoning
                         about networks of mobile agents broadcasting
                         messages to other agents following some (evolving)
                         communication topology. The parameterized
                         verification of such models aims at checking whether
                         a given property holds irrespective of the initial
                         configuration (number of agents, initial states and
                         initial communication topology). We~focus here on
                         the \emph{synchronization property}, asking whether
                         all agents converge to a set of target states after
                         some execution. This~problem is known to be
                         decidable in polynomial time when no constraints are
                         imposed on the evolution of the communication
                         topology (while~it~is undecidable for static
                         broadcast networks).\par In this paper we
                         investigate how various constraints on
                         reconfigurations affect the decidability and
                         complexity of the synchronization problem.
                         In~particular, we show that when bounding the number
                         of reconfigured links between two communications
                         steps by a constant, synchronization becomes
                         undecidable; on~the other hand, synchronization
                         remains decidable in PTIME when the bound grows with
                         the number of agents.},
}

@inproceedings{csl2015-BBMR,
  author =              {Brihaye, {\relax Th}omas and Bruy{\`e}re,
                         V{\'e}ronique and Meunier, No{\"e}mie and Raskin,
                         Jean-Fran{\c c}ois},
  title =               {Weak Subgame Perfect Equilibria and their
                         Application to Quantitative Reachability},
  editor =              {Kreutzer, Stephan},
  booktitle =           {{P}roceedings of the 24th {EACSL} {A}nnual
                         {C}onference on {C}omputer {S}cience {L}ogic
                         ({CSL}'15)},
  acronym =             {{CSL}'15},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {41},
  pages =               {504-518},
  year =                {2015},
  month =               sep,
  doi =                 {10.4230/LIPIcs.CSL.2015.504},
}

Abstract

We study the problem of the existence (and computation) of Nash equilibria in multi-player concurrent games with Büchi-definable objectives. First, when the objectives are Büchi conditions on the game, we prove that the existence problem can be solved in polynomial time. In a second part, we extend our technique to objectives defined by deterministic Büchi automata, and prove that the problem then becomes EXPTIME-complete. We prove PSPACE-completeness for the case where the Büchi automata are 1-weak.

@inproceedings{fsttcs2011-BBMU,
  author =              {Bouyer, Patricia and Brenguier, Romain and Markey,
                         Nicolas and Ummels, Michael},
  title =               {{N}ash Equilibria in Concurrent Games with
                         {B}{\"u}chi Objectives},
  editor =              {Chakraborty, Supratik and Kumar, Amit},
  booktitle =           {{P}roceedings of the 31st {C}onference on
                         {F}oundations of {S}oftware {T}echnology and
                         {T}heoretical {C}omputer {S}cience ({FSTTCS}'11)},
  acronym =             {{FSTTCS}'11},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {13},
  pages =               {375-386},
  year =                {2011},
  month =               dec,
  doi =                 {10.4230/LIPIcs.FSTTCS.2011.375},
  abstract =            {We study the problem of the existence (and
                         computation) of Nash equilibria in multi-player
                         concurrent games with B{\"u}chi-definable
                         objectives. First, when the objectives are B{\"u}chi
                         conditions on the game, we prove that the existence
                         problem can be solved in polynomial time. In a
                         second part, we extend our technique to objectives
                         defined by deterministic B{\"u}chi automata, and
                         prove that the problem then becomes
                         EXPTIME-complete. We prove PSPACE-completeness for
                         the case where the B{\"u}chi automata are 1-weak.},
}

Abstract

We consider concurrent games played on graphs, in which each player has several qualitative (e.g. reachability or Büchi) objectives, and a preorder on these objectives (for instance the counting order, where the aim is to maximise the number of objectives that are fulfilled).

We study two fundamental problems in that setting: (1) the value problem, which aims at deciding the existence of a strategy that ensures a given payoff; (2) the Nash equilibrium problem, where we want to decide the existence of a Nash equilibrium (possibly with a condition on the payoffs). We characterise the exact complexities of these problems for several relevant preorders, and several kinds of objectives.

@inproceedings{fossacs2012-BBMU,
  author =              {Bouyer, Patricia and Brenguier, Romain and Markey,
                         Nicolas and Ummels, Michael},
  title =               {Concurrent games with ordered objectives},
  editor =              {Birkedal, Lars},
  booktitle =           {{P}roceedings of the 15th {I}nternational
                         {C}onference on {F}oundations of {S}oftware
                         {S}cience and {C}omputation {S}tructure
                         ({FoSSaCS}'12)},
  acronym =             {{FoSSaCS}'12},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {7213},
  pages =               {301-315},
  year =                {2012},
  month =               mar,
  doi =                 {10.1007/978-3-642-28729-9_20},
  abstract =            {We consider concurrent games played on graphs, in
                         which each player has several qualitative (e.g.
                         reachability or B{\"u}chi) objectives, and a
                         preorder on these objectives (for instance the
                         counting order, where the aim is to maximise the
                         number of objectives that are fulfilled).\par We
                         study two fundamental problems in that setting:
                         (1)~the \emph{value problem}, which aims at deciding
                         the existence of a strategy that ensures a given
                         payoff; (2)~the \emph{Nash equilibrium problem},
                         where we want to decide the existence of a Nash
                         equilibrium (possibly with a condition on the
                         payoffs). We characterise the exact complexities of
                         these problems for several relevant preorders, and
                         several kinds of objectives.},
}

Abstract

We study pure-strategy Nash equilibria in multiplayer concurrent games, for a variety of omega-regular objectives. For simple objectives (e.g. reachability, Büchi objectives), we transform the problem of deciding the existence of a Nash equilibrium in a given concurrent game into that of deciding the existence of a winning strategy in a turn-based two-player game (with a refined objective). We use that transformation to design algorithms for computing Nash equilibria, which in most cases have optimal worst-case complexity. For automata-defined objectives, we extend the above algorithms using a simulation relation which allows us to consider the product of the game with the automata defining the objectives. Building on previous algorithms for simple qualitative objectives, we define and study a semi-quantitative framework, where all players have several boolean objectives equipped with a preorder; a player may for instance want to satisfy all her objectives, or to maximise the number of objectives that she achieves. In most cases, we prove that the algorithms we obtain match the complexity of the problem they address.

@article{lmcs11(2)-BBMU,
  author =              {Bouyer, Patricia and Brenguier, Romain and Markey,
                         Nicolas and Ummels, Michael},
  title =               {Pure {N}ash Equilibria in Concurrent Games},
  journal =             {Logical Methods in Computer Science},
  volume =              {11},
  number =              {2:9},
  year =                {2015},
  month =               jun,
  doi =                 {10.2168/LMCS-11(2:9)2015},
  abstract =            {We study pure-strategy Nash equilibria in
                         multiplayer concurrent games, for a variety of
                         omega-regular objectives. For simple objectives
                         (e.g. reachability, B{\"u}chi objectives), we
                         transform the problem of deciding the existence of a
                         Nash equilibrium in a given concurrent game into
                         that of deciding the existence of a winning strategy
                         in a turn-based two-player game (with a refined
                         objective). We use that transformation to design
                         algorithms for computing Nash equilibria, which in
                         most cases have optimal worst-case complexity. For
                         automata-defined objectives, we extend the above
                         algorithms using a simulation relation which allows
                         us to consider the product of the game with the
                         automata defining the objectives. Building on
                         previous algorithms for simple qualitative
                         objectives, we define and study a semi-quantitative
                         framework, where all players have several boolean
                         objectives equipped with a preorder; a player may
                         for instance want to satisfy all her objectives, or
                         to maximise the number of objectives that she
                         achieves. In most cases, we prove that the
                         algorithms we obtain match the complexity of the
                         problem they address.},
}

@inproceedings{formats2004-BBR,
  author =              {Brihaye, {\relax Th}omas and Bruy{\`e}re,
                         V{\'e}ronique and Raskin, Jean-Fran{\c c}ois},
  title =               {Model-checking for weighted timed automata},
  editor =              {Lakhnech, Yassine and Yovine, Sergio},
  booktitle =           {{P}roceedings of the {J}oint {I}nternational
                         {C}onferences on {F}ormal {M}odelling and {A}nalysis
                         of {T}imed {S}ystems ({FORMATS}'04) and {F}ormal
                         {T}echniques in {R}eal-Time and {F}ault-Tolerant
                         {S}ystems ({FTRTFT}'04)},
  acronym =             {{FORMATS-FTRTFT}'04},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {3253},
  pages =               {277-292},
  year =                {2004},
  month =               sep,
}

@inproceedings{formats2005-BBR,
  author =              {Brihaye, {\relax Th}omas and Bruy{\`e}re,
                         V{\'e}ronique and Raskin, Jean-Fran{\c c}ois},
  title =               {On Optimal Timed Strategies},
  editor =              {Pettersson, Paul and Yi, Wang},
  booktitle =           {{P}roceedings of the 3rd {I}nternational
                         {C}onferences on {F}ormal {M}odelling and {A}nalysis
                         of {T}imed {S}ystems ({FORMATS}'05)},
  acronym =             {{FORMATS}'05},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {3829},
  pages =               {49-64},
  year =                {2005},
  month =               sep,
  doi =                 {10.1007/11603009_5},
}

@inproceedings{spin2001-BBS,
  author =              {Barnat, Ji{\v r}{\'\i} and Brim, Lubo{\v s} and
                         St{\v r}{\'\i}brn{\'a}, Jitka},
  title =               {Distributed {LTL} Model-Checking in {SPIN}},
  editor =              {Dwyer, Matthew B.},
  booktitle =           {{P}roceedings of the 8th {I}nternational {SPIN}
                         {W}orkshop ({SPIN}'01)},
  acronym =             {{SPIN}'01},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2057},
  pages =               {200-216},
  year =                {2001},
  month =               may,
}

@inproceedings{tacas2003-BC,
  author =              {Benedetti, Marco and Cimatti, Alessandro},
  title =               {Bounded Model Checking for Past {LTL}},
  editor =              {Garavel, Hubert and Hatcliff, John},
  booktitle =           {{P}roceedings of the 9th {I}nternational
                         {C}onference on {T}ools and {A}lgorithms for
                         {C}onstruction and {A}nalysis of {S}ystems
                         ({TACAS}'03)},
  acronym =             {{TACAS}'03},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2619},
  pages =               {18-33},
  year =                {2003},
  month =               apr,
}

@article{jalc10(4)-BC,
  author =              {Bouyer, Patricia and Chevalier, Fabrice},
  title =               {On Conciseness of Extensions of Timed Automata},
  journal =             {Journal of Automata, Languages and Combinatorics},
  volume =              {10},
  number =              {4},
  pages =               {393-405},
  year =                {2005},
}

@article{eatcs-bull89()-BC,
  author =              {Bouyer, Patricia and Chevalier, Fabrice},
  title =               {On the Control of Timed and Hybrid Systems},
  publisher =           {EATCS},
  journal =             {EATCS Bulletin},
  volume =              {89},
  pages =               {79-96},
  year =                {2006},
  month =               jun,
}

@techreport{FIMU-RS-2010-03-BC,
  author =              {Brim, Lubo{\v s} and Chaloupka, Jakub},
  title =               {Using Strategy Improvement to Stay Alive},
  number =              {FIMU-RS-2010-03},
  year =                {2010},
  month =               mar,
  institution =         {Faculty of Informatics, Masaryk University, Brno,
                         Czech Republic},
}

@inproceedings{compos1997-BCC,
  author =              {Berezin, Sergey and Campos, S{\'e}rgio Vale Aguiar
                         and Clarke, Edmund M.},
  title =               {Compositional Reasoning in Model Checking},
  editor =              {de Roever, Willem-Paul and Langmaack, Hans and
                         Pnueli, Amir},
  booktitle =           {{R}evised {L}ectures of the 1st {I}nternational
                         {S}ymposium on {C}ompositionality: {T}he
                         {S}ignificant {D}ifference ({COMPOS}'97)},
  acronym =             {{COMPOS}'97},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {1536},
  pages =               {81-102},
  year =                {1998},
  confyear =            {1997},
  confmonth =           {9},
}

@incollection{AC58-BCCSZ,
  author =              {Biere, Armin and Cimatti, Alessandro and Clarke,
                         Edmund M. and Strichman, Ofer and Zhu, Yunshan},
  title =               {Bounded Model Checking},
  editor =              {Zelkowitz, Marvin},
  booktitle =           {Highly Dependable Software},
  publisher =           {Academic Press},
  series =              {Advances in Computers},
  volume =              {58},
  pages =               {117-148},
  chapter =             {3},
  year =                {2003},
}

@inproceedings{tacas1999-BCCZ,
  author =              {Biere, Armin and Cimatti, Alessandro and Clarke,
                         Edmund M. and Zhu, Yunshan},
  title =               {Symbolic Model Checking without {BDD}s},
  editor =              {Cleaveland, Rance},
  booktitle =           {{P}roceedings of the 5th {I}nternational
                         {C}onference on {T}ools and {A}lgorithms for
                         {C}onstruction and {A}nalysis of {S}ystems
                         ({TACAS}'99)},
  acronym =             {{TACAS}'99},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {1579},
  pages =               {193-207},
  year =                {1999},
  month =               mar,
}

@inproceedings{fossacs2005-BCD,
  author =              {Bouyer, Patricia and Chevalier, Fabrice and D'Souza,
                         Deepak},
  title =               {Fault Diagnosis Using Timed Automata},
  editor =              {Sassone, Vladimiro},
  booktitle =           {{P}roceedings of the 8th {I}nternational
                         {C}onference on {F}oundations of {S}oftware
                         {S}cience and {C}omputation {S}tructure
                         ({FoSSaCS}'05)},
  acronym =             {{FoSSaCS}'05},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {3441},
  pages =               {219-233},
  year =                {2005},
  month =               apr,
  doi =                 {10.1007/978-3-540-31982-5_14},
}

@inproceedings{cav2007-BCDFLL,
  author =              {Behrmann, Gerd and Cougnard, Agn{\`e}s and David,
                         Alexandre and Fleury, Emmanuel and Larsen, Kim
                         Guldstrand and Lime, Didier},
  title =               {{UPPAAL-Tiga}: Time for Playing Games!},
  editor =              {Damm, Werner and Hermanns, Holger},
  booktitle =           {{P}roceedings of the 19th {I}nternational
                         {C}onference on {C}omputer {A}ided {V}erification
                         ({CAV}'07)},
  acronym =             {{CAV}'07},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {4590},
  pages =               {121-125},
  year =                {2007},
  month =               jul,
}

@article{fmsd38(2)-BCDGR,
  author =              {Brim, Lubo{\v s} and Chaloupka, Jakub and Doyen,
                         Laurent and Gentilini, Raffaella and Raskin,
                         Jean-Fran{\c c}ois},
  title =               {Faster algorithms for mean-payoff games},
  publisher =           {Springer-Verlag},
  journal =             {Formal Methods in System Design},
  volume =              {38},
  number =              {2},
  pages =               {97-118},
  year =                {2011},
  month =               apr,
  doi =                 {10.1007/s10703-010-0105-x},
}

@article{ijrr17(4)-BCEKPST,
  author =              {Borrelly, Jean-Jacques and Costemaniere, {\`E}ve and
                         Espiau, Bernard and Kapellos, Konstantinos and
                         Pissard{-}Gibollet, Roger and Simon, Daniel and
                         Turro, Nicolas},
  title =               {The {ORCCAD} Architecture},
  journal =             {International Journal of Robotics Research},
  volume =              {17},
  number =              {4},
  pages =               {338-359},
  year =                {1998},
  month =               apr,
}

@inproceedings{stacs2003-BCF,
  author =              {Buhrman, Harry and Chang, Richard and Fortnow,
                         Lance},
  title =               {One Bit of Advice},
  editor =              {Alt, Helmut and Habib, Michel},
  booktitle =           {{P}roceedings of the 20th {S}ymposium on
                         {T}heoretical {A}spects of {C}omputer {S}cience
                         ({STACS}'03)},
  acronym =             {{STACS}'03},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2607},
  pages =               {547-558},
  year =                {2003},
  month =               feb,
}

@inproceedings{fsttcs2004-BCFL,
  author =              {Bouyer, Patricia and Cassez, Franck and Fleury,
                         Emmanuel and Larsen, Kim Guldstrand},
  title =               {Optimal Strategies in Priced Timed Game Automata},
  editor =              {Lodaya, Kamal and Mahajan, Meena},
  booktitle =           {{P}roceedings of the 24th {C}onference on
                         {F}oundations of {S}oftware {T}echnology and
                         {T}heoretical {C}omputer {S}cience ({FSTTCS}'04)},
  acronym =             {{FSTTCS}'04},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {3328},
  pages =               {148-160},
  year =                {2004},
  month =               dec,
}

@techreport{TR-brics04-4,
  author =              {Bouyer, Patricia and Cassez, Franck and Fleury,
                         Emmanuel and Larsen, Kim Guldstrand},
  title =               {Optimal Strategies in Priced Timed Games},
  number =              {RS-04-4},
  year =                {2004},
  month =               feb,
  institution =         {Basic Research in Computer Science, Aalborg
                         University, Denmark},
  type =                {Research Report},
}

@article{tcs59(1-2)-BCG,
  author =              {Browne, Michael C. and Clarke, Edmund M. and
                         Grumberg, Orna},
  title =               {Characterizing Finite {K}ripke Structures in
                         Propositional Temporal Logic},
  publisher =           {Elsevier},
  journal =             {Theoretical Computer Science},
  volume =              {59},
  number =              {1-2},
  pages =               {115-131},
  year =                {1988},
  month =               jul,
}

@article{siamcomp21(4)-BCGR,
  author =              {Buss, Samuel R. and Cook, Stephen A. and Gupta,
                         Vineet and Ramachandran, Vijaya},
  title =               {An Optimal Parallel Algorithm for Formula
                         Evaluation},
  publisher =           {Society for Industrial and Applied Math.},
  journal =             {SIAM Journal on Computing},
  volume =              {21},
  number =              {4},
  pages =               {755-780},
  year =                {1992},
  month =               aug,
}

@inproceedings{lics2011-BCHK,
  author =              {Boker, Udi and Chatterjee, Krishnendu and Henzinger,
                         Thomas A. and Kupferman, Orna},
  title =               {Temporal Specifications with Accumulative Values},
  booktitle =           {{P}roceedings of the 26th {A}nnual {S}ymposium on
                         {L}ogic in {C}omputer {S}cience ({LICS}'11)},
  acronym =             {{LICS}'11},
  publisher =           {IEEE Comp. Soc. Press},
  pages =               {43-52},
  year =                {2011},
  month =               jun,
  doi =                 {10.1109/LICS.2011.33},
}

@article{tocl15(4)-BCHK,
  author =              {Boker, Udi and Chatterjee, Krishnendu and Henzinger,
                         Thomas A. and Kupferman, Orna},
  title =               {Temporal Specifications with Accumulative Values},
  publisher =           {ACM Press},
  journal =             {ACM Transactions on Computational Logic},
  volume =              {15},
  number =              {4},
  pages =               {27:1-27:25},
  year =                {2014},
  month =               aug,
  doi =                 {10.1145/2629686},
}

@inproceedings{fsttcs2001-BCKP,
  author =              {Brim, Lubo{\v s} and {\v{C}}erna, Ivana and
                         Kr{\v{c}}{\'a}l, Pavel and Pel{\'a}nek, Radek},
  title =               {Distributed {LTL} Model Checking Based on Negative
                         Cycle Detection},
  editor =              {Hariharan, Ramesh and Mukund, Madhavan and Vinay,
                         V.},
  booktitle =           {{P}roceedings of the 21st {C}onference on
                         {F}oundations of {S}oftware {T}echnology and
                         {T}heoretical {C}omputer {S}cience ({FSTTCS}'01)},
  acronym =             {{FSTTCS}'01},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2245},
  pages =               {96-107},
  year =                {2001},
  month =               dec,
}

Abstract

TPTL and MTL are two classical timed extensions of LTL. In this paper, we positively answer a 15-year-old conjecture that TPTL is strictly more expressive than MTL. But we show that, surprisingly, the TPTL formula proposed by Alur and Henzinger for witnessing this conjecture can be expressed in MTL. More generally, we show that TPTL formulae using only the F modality can be translated into MTL.

@inproceedings{fsttcs2005-BCM,
  author =              {Bouyer, Patricia and Chevalier, Fabrice and Markey,
                         Nicolas},
  title =               {On the Expressiveness of {TPTL} and {MTL}},
  editor =              {Ramanujam, R. and Sen, Sandeep},
  booktitle =           {{P}roceedings of the 25th {C}onference on
                         {F}oundations of {S}oftware {T}echnology and
                         {T}heoretical {C}omputer {S}cience ({FSTTCS}'05)},
  acronym =             {{FSTTCS}'05},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {3821},
  pages =               {432-443},
  year =                {2005},
  month =               dec,
  doi =                 {10.1007/11590156_35},
  abstract =            {TPTL and MTL are two classical timed extensions of
                         LTL. In this paper, we positively answer a
                         15-year-old conjecture that TPTL is strictly more
                         expressive than MTL. But we show that, surprisingly,
                         the TPTL formula proposed by Alur and Henzinger for
                         witnessing this conjecture can be expressed in MTL.
                         More generally, we show that TPTL formulae using
                         only the \textbf{F} modality can be translated into
                         MTL.},
}

Abstract

TPTL and MTL are two classical timed extensions of LTL. In this paper, we prove the 20-year-old conjecture that TPTL is strictly more expressive than MTL. But we show that, surprisingly, the TPTL formula proposed by Alur and Henzinger for witnessing this conjecture can be expressed in MTL. More generally, we show that TPTL formulae using only modality F can be translated into MTL.

@article{icomp208(2)-BCM,
  author =              {Bouyer, Patricia and Chevalier, Fabrice and Markey,
                         Nicolas},
  title =               {On the Expressiveness of {TPTL} and {MTL}},
  publisher =           {Elsevier},
  journal =             {Information and Computation},
  volume =              {208},
  number =              {2},
  pages =               {97-116},
  year =                {2010},
  month =               feb,
  doi =                 {10.1016/j.ic.2009.10.004},
  abstract =            {TPTL and MTL are two classical timed extensions
                         of~LTL. In~this paper, we prove the 20-year-old
                         conjecture that TPTL is strictly more expressive
                         than~MTL. But we show that, surprisingly, the
                         TPTL~formula proposed by Alur and Henzinger for
                         witnessing this conjecture \emph{can} be expressed
                         in~MTL. More generally, we show that TPTL formulae
                         using only modality~F can be translated into~MTL.},
}

Abstract

Weighted timed automata have been defined in the early 2000's for modelling resource-consumption or -allocation problems in real-time systems. Optimal reachability is decidable in weighted timed automata, and a symbolic forward algorithm has been developed to solve that problem. This algorithm uses so-called priced zones, an extension of standard zones with cost functions. In order to ensure termination, the algorithm requires clocks to be bounded. For unpriced timed automata, much work has been done to develop sound abstractions adapted to the forward exploration of timed automata, ensuring termination of the model-checking algorithm without bounding the clocks. In this paper, we take advantage of recent developments on abstractions for timed automata, and propose an algorithm allowing for symbolic analysis of all weighted timed automata, without requiring bounded clocks.

@inproceedings{cav2016-BCM,
  author =              {Bouyer, Patricia and Colange, Maximilien and Markey,
                         Nicolas},
  title =               {Symbolic Optimal Reachability in Weighted Timed
                         Automata},
  editor =              {Chaudhuri, Swarat and Farzan, Azadeh},
  booktitle =           {{P}roceedings of the 28th {I}nternational
                         {C}onference on {C}omputer {A}ided {V}erification
                         ({CAV}'16)},
  acronym =             {{CAV}'16},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9779},
  pages =               {513-530},
  year =                {2016},
  month =               jul,
  doi =                 {10.1007/978-3-319-41528-4_28},
  url =                 {http://arxiv.org/abs/1602.00481},
  abstract =            {Weighted timed automata have been defined in the
                         early 2000's for modelling resource-consumption or
                         -allocation problems in real-time systems. Optimal
                         reachability is decidable in weighted timed
                         automata, and a symbolic forward algorithm has been
                         developed to solve that problem. This algorithm uses
                         so-called priced zones, an extension of standard
                         zones with cost functions. In order to ensure
                         termination, the algorithm requires clocks to be
                         bounded. For unpriced timed automata, much work has
                         been done to develop sound abstractions adapted to
                         the forward exploration of timed automata, ensuring
                         termination of the model-checking algorithm without
                         bounding the clocks. In this paper, we take
                         advantage of recent developments on abstractions for
                         timed automata, and propose an algorithm allowing
                         for symbolic analysis of all weighted timed
                         automata, without requiring bounded clocks.},
}

@article{icomp98(2)-BCMDH,
  author =              {Burch, Jerry R. and Clarke, Edmund M. and McMillan,
                         Kenneth L. and Dill, David L. and Hwang, L. J.},
  title =               {Symbolic model checking: {\(10^{20}\)} states and
                         beyond},
  publisher =           {Academic Press},
  journal =             {Information and Computation},
  volume =              {98},
  number =              {2},
  pages =               {142-170},
  year =                {1992},
  month =               jun,
}

@book{BCOQ-des2001,
  author =              {Baccelli, Fran{\c c}ois and Cohen, Guy and Olsder,
                         Geert Jan and Quadrat, Jean-Pierre},
  title =               {Shynchronization and Linearity. An Algebra For
                         Discrete Event Systems},
  publisher =           {John Wiley \& Sons},
  year =                {1992},
  url =                 {http://www-rocq.inria.fr/metalau/cohen/SED/book-online.html},
}

@inproceedings{smc1999-BCZ,
  author =              {Biere, Armin and Clarke, Edmund M. and Zhu, Yunshan},
  title =               {Combining Local and Global Model Checking},
  editor =              {Cimatti, Alessandro and Grumberg, Orna},
  booktitle =           {{P}roceedings of the 1st {I}nternational {W}orkshop
                         on {S}ymbolic {M}odel {C}hecking ({SMC}'99)},
  acronym =             {{SMC}'99},
  publisher =           {Elsevier},
  series =              {Electronic Notes in Theoretical Computer Science},
  volume =              {23},
  number =              {2},
  year =                {1999},
  month =               jul,
}

@article{ipl75(1-2)-BD,
  author =              {B{\'e}rard, B{\'e}atrice and Dufourd, Catherine},
  title =               {Timed Automata and Additive Clock Constraints},
  publisher =           {Elsevier},
  journal =             {Information Processing Letters},
  volume =              {75},
  number =              {1-2},
  pages =               {1-7},
  year =                {2000},
  month =               jul,
}

@article{tcs321(2-3)-BDFP,
  author =              {Bouyer, Patricia and Dufourd, Catherine and Fleury,
                         Emmanuel and Petit, Antoine},
  title =               {Updatable timed Automata},
  publisher =           {Elsevier},
  journal =             {Theoretical Computer Science},
  volume =              {321},
  number =              {2-3},
  pages =               {291-345},
  year =                {2004},
  month =               aug,
  doi =                 {10.1016/j.tcs.2004.04.003},
}

@inproceedings{concur2017-BDGG,
  author =              {Bertrand, Nathalie and Dewaskar, Miheer and Genest,
                         Blaise and Gimbert, Hugo},
  title =               {Controlling a population},
  editor =              {Meyer, Roland and Nestmann, Uwe},
  booktitle =           {{P}roceedings of the 28th {I}nternational
                         {C}onference on {C}oncurrency {T}heory
                         ({CONCUR}'17)},
  acronym =             {{CONCUR}'17},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {85},
  pages =               {12:1-12:16},
  year =                {2017},
  month =               sep,
  doi =                 {10.4230/LIPIcs.CONCUR.2017.12},
}

@inproceedings{icalp2011(2)-BDGORW,
  author =              {Brihaye, {\relax Th}omas and Doyen, Laurent and
                         Geeraerts, Gilles and Ouaknine, Jo{\"e}l and Raskin,
                         Jean-Fran{\c c}ois and Worrell, James},
  title =               {On Reachability for Hybrid Automata over Bounded
                         Time},
  editor =              {Aceto, Luca and Henzinger, Monika and Sgall, Ji{\v
                         r}{\'\i}},
  booktitle =           {{P}roceedings of the 38th {I}nternational
                         {C}olloquium on {A}utomata, {L}anguages and
                         {P}rogramming ({ICALP}'11)~-- Part~{II}},
  acronym =             {{ICALP}'11},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {6756},
  pages =               {416-427},
  year =                {2011},
  month =               jul,
}

@article{fundi36(2-3)-BDGP,
  author =              {B{\'e}rard, B{\'e}atrice and Diekert, Volker and
                         Gastin, Paul and Petit, Antoine},
  title =               {Characterization of the Expressive Power of Silent
                         Transitions in Timed Automata},
  publisher =           {IOS Press},
  journal =             {Fundamenta Informaticae},
  volume =              {36},
  number =              {2-3},
  pages =               {145-182},
  year =                {1998},
  month =               nov,
}

@inproceedings{stacs2006-BDHK,
  author =              {Berwanger, Dietmar and Dawar, Anuj and Hunter, Paul
                         and Kreutzer, Stephan},
  title =               {{DAG}-Width and Parity Games},
  editor =              {Durand, Bruno and Thomas, Wolfgang},
  booktitle =           {{P}roceedings of the 23rd {S}ymposium on
                         {T}heoretical {A}spects of {C}omputer {S}cience
                         ({STACS}'06)},
  acronym =             {{STACS}'06},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {3884},
  pages =               {524-536},
  year =                {2006},
  month =               feb,
  doi =                 {10.1007/11672142_43},
}

@proceedings{cassting-syncop2016-DJMS,
  title =               {{P}roceedings of the {C}assting Workshop on {G}ames
                         for the {S}ynthesis of {C}omplex {S}ystems
                         ({C}assting'16) and of the 3rd {I}nternational
                         {W}orkshop on {S}ynthesis of {C}omplex {P}arameters
                         ({S}yn{C}o{P}'16)},
  editor =              {Brihaye, {\relax Th}omas and Delahaye, Beno{\^\i}t
                         and Jezequel, Lo{\"\i}g and Markey, Nicolas and
                         Srba, Ji{\v r}{\'\i}},
  booktitle =           {{P}roceedings of the {C}assting Workshop on {G}ames
                         for the {S}ynthesis of {C}omplex {S}ystems
                         ({C}assting'16) and of the 3rd {I}nternational
                         {W}orkshop on {S}ynthesis of {C}omplex {P}arameters
                         ({S}yn{C}o{P}'16)},
  acronym =             {{C}assting{{\slash}}{S}yn{C}o{P}'16},
  series =              {Electronic Proceedings in Theoretical Computer
                         Science},
  volume =              {220},
  year =                {2016},
  month =               jul,
  confyear =            {2016},
  confmonth =           {4},
  doi =                 {10.4204/EPTCS.220},
  url =                 {http://eptcs.web.cse.unsw.edu.au/
                         content.cgi?CASSTINGSynCoP2016},
}

@inproceedings{sfm2004-BDL,
  author =              {Behrmann, Gerd and David, Alexandre and Larsen, Kim
                         Guldstrand},
  title =               {A~Tutorial on {U}ppaal},
  editor =              {Bernardo, Marco and Corradini, Flavio},
  booktitle =           {{F}ormal {M}ethods for the {D}esign of {R}eal-{T}ime
                         {S}ystems~--- {R}evised {L}ectures of the
                         {I}nternational {S}chool on {F}ormal {M}ethods for
                         the {D}esign of {C}omputer, {C}ommunication and
                         {S}oftware {S}ystems ({SFM-RT}'04)},
  acronym =             {{SFM-RT}'04},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {3185},
  pages =               {200-236},
  year =                {2004},
  month =               sep,
  doi =                 {10.1007/978-3-540-30080-9_7},
}

@inproceedings{tase2012-BDL,
  author =              {Bollig, Benedikt and Decker, Normann and Leucker,
                         Martin},
  title =               {Frequency Linear-time Temporal Logic},
  editor =              {Margaria, Tiziana and Qiu, Zongyang and Yang,
                         Hongli},
  booktitle =           {{P}roceedings of the 6th {I}nternational {S}ymposium
                         on {T}heoretical {A}spects of {S}oftware
                         {E}ngineering ({TASE}'12)},
  acronym =             {{TASE}'12},
  publisher =           {IEEE Comp. Soc. Press},
  pages =               {85-92},
  year =                {2012},
  month =               jul,
  doi =                 {10.1109/TASE.2012.43},
}

@inproceedings{qest2006-BDLHPYH,
  author =              {Behrmann, Gerd and David, Alexandre and Larsen, Kim
                         Guldstrand and H{\aa}kansson, John and Pettersson,
                         Paul and Yi, Wang and Hendriks, Martijn},
  title =               {UPPAAL~4.0},
  booktitle =           {{P}roceedings of the 3rd {I}nternational
                         {C}onference on {Q}uantitative {E}valuation of
                         {S}ystems ({QEST}'06)},
  acronym =             {{QEST}'06},
  publisher =           {IEEE Comp. Soc. Press},
  pages =               {125-126},
  year =                {2006},
  month =               sep,
  doi =                 {10.1109/QEST.2006.59},
}

@article{acta51(3-4)-BDLL,
  author =              {Bulychev, Peter and David, Alexandre and Larsen, Kim
                         Guldstrand and Li, Guangyuan},
  title =               {Efficient Controller Synthesis for a fragment of
                         {{\(\textsf{MTL}_{0,\infty}\)}}},
  publisher =           {Springer-Verlag},
  journal =             {Acta Informatica},
  volume =              {51},
  number =              {3-4},
  pages =               {165-192},
  year =                {2014},
  month =               jun,
  doi =                 {10.1007/s00236-013-0189-z},
}

@inproceedings{lpar2012-BDLLLPS,
  author =              {Bulychev, Peter and David, Alexandre and Larsen, Kim
                         Guldstrand and Legay, Axel and Li, Guangyuan and
                         Poulsen, Danny B{\o}gsted and Stainer, Am{\'e}lie},
  title =               {Monitor-based statistical model checking for
                         weighted metric temporal logic},
  editor =              {Bj{\o}rner, Nikolaj and Voronkov, Andrei},
  booktitle =           {{P}roceedings of the 18th {I}nternational
                         {C}onference {L}ogic {P}rogramming and {A}utomated
                         {R}easoning ({LPAR}'12)},
  acronym =             {{LPAR}'12},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {7180},
  pages =               {168-182},
  year =                {2012},
  month =               mar,
  doi =                 {10.1007/978-3-642-28717-6_15},
}

@inproceedings{nasaFM2012-BDLLMP,
  author =              {Bulychev, Peter and David, Alexandre and Larsen, Kim
                         Guldstrand and Legay, Axel and Miku{\v{c}}ionis,
                         Marius and Poulsen, Danny B{\o}gsted},
  title =               {Checking and Distributing Statistical Model
                         Checking},
  editor =              {Goodloe, Alwyn and Person, Suzette},
  booktitle =           {{P}roceedings of the 4th {NASA} {F}ormal {M}ethods
                         {S}ymposium ({NFM}'12)},
  acronym =             {{NFM}'12},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {7226},
  pages =               {449-463},
  year =                {2012},
  month =               apr,
}

Abstract

We extend the alternating-time temporal logics ATL and ATL* with strategy contexts and memory constraints: the first extension make strategy quantifiers to not "forget" the strategies being executed by the other players. The second extension allows strategy quantifiers to restrict to memoryless or bounded-memory strategies.

We first consider expressiveness issues. We show that our logics can express important properties such as equilibria, and we formally compare them with other similar formalisms (ATL, ATL*, Game Logic, Strategy Logic, ...). We then address the problem of model-checking for our logics, providing a PSPACE algoritm for the sublogics involving only memoryless strategies and an EXPSPACE algorithm for the bounded-memory case.

@inproceedings{lfcs2009-BDLM,
  author =              {Brihaye, {\relax Th}omas and Da{~}Costa, Arnaud and
                         Laroussinie, Fran{\c c}ois and Markey, Nicolas},
  title =               {{ATL} with Strategy Contexts and Bounded Memory},
  editor =              {Artemov, Sergei N. and Nerode, Anil},
  booktitle =           {{P}roceedings of the {I}nternational {S}ymposium
                         {L}ogical {F}oundations of {C}omputer {S}cience
                         ({LFCS}'09)},
  acronym =             {{LFCS}'09},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {5407},
  pages =               {92-106},
  year =                {2009},
  month =               jan,
  doi =                 {10.1007/978-3-540-92687-0_7},
  abstract =            {We extend the alternating-time temporal logics ATL
                         and ATL\textsuperscript{*} with \emph{strategy
                         contexts} and \emph{memory constraints}: the first
                         extension make strategy quantifiers to not
                         {"}forget{"} the strategies being executed by the
                         other players. The second extension allows strategy
                         quantifiers to restrict to memoryless or
                         bounded-memory strategies.\par We first consider
                         expressiveness issues. We show that our logics can
                         express important properties such as equilibria, and
                         we formally compare them with other similar
                         formalisms (ATL, ATL\textsuperscript{*}, Game Logic,
                         Strategy Logic,~...). We~then address the problem of
                         model-checking for our logics, providing a PSPACE
                         algoritm for the sublogics involving only memoryless
                         strategies and an EXPSPACE algorithm for the
                         bounded-memory case.},
}

@inproceedings{coco1997-BDLMT,
  author =              {Berman, Joshua and Drisko, Arthur and Lemieux,
                         Fran{\c c}ois and Moore, Cristopher and Th{\'e}rien,
                         Denis},
  title =               {Circuit and Expressions with Non-Associative Gates},
  booktitle =           {{P}roceedings of the 12th {A}nnual {IEEE}
                         {C}onference on {C}omputational {C}omplexity
                         ({CoCo}'97)},
  acronym =             {{CoCo}'97},
  publisher =           {IEEE Comp. Soc. Press},
  pages =               {193-203},
  year =                {1997},
  month =               jun,
}

@article{spe41(2)-ADGPY,
  author =              {Behrmann, Gerd and David, Alexandre and Larsen, Kim
                         Guldstrand and Pettersson, Paul and Yi, Wang},
  title =               {Developing {UPPAAL} over 15~years},
  publisher =           {IEEE Comp. Soc. Press},
  journal =             {Software~-- Practice and Experience},
  volume =              {41},
  number =              {2},
  pages =               {133-142},
  year =                {2011},
  month =               feb,
}

@inproceedings{cav2003-BDMP,
  author =              {Bouyer, Patricia and D'Souza, Deepak and Madhusudan,
                         Parthasarathy and Petit, Antoine},
  title =               {Timed Control with Partial Observability},
  editor =              {Hunt, Jr, Warren A. and Somenzi, Fabio},
  booktitle =           {{P}roceedings of the 15th {I}nternational
                         {C}onference on {C}omputer {A}ided {V}erification
                         ({CAV}'03)},
  acronym =             {{CAV}'03},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2725},
  pages =               {180-192},
  year =                {2003},
  month =               jul,
}

Abstract

In this paper, we extend the classical notion of strategies in turn-based finite games by allowing several moves to be selected. We define and study a quantitative measure for permissivity of such strategies by assigning penalties when blocking transitions. We prove that for reachability objectives, most permissive strategies exist, can be chosen memoryless, and can be computed in polynomial time, while it is in NP∩coNP for discounted and mean penalties.

@inproceedings{concur2009-BDMR,
  author =              {Bouyer, Patricia and Duflot, Marie and Markey,
                         Nicolas and Renault, Gabriel},
  title =               {Measuring Permissivity in Finite Games},
  editor =              {Bravetti, Mario and Zavattaro, Gianluigi},
  booktitle =           {{P}roceedings of the 20th {I}nternational
                         {C}onference on {C}oncurrency {T}heory
                         ({CONCUR}'09)},
  acronym =             {{CONCUR}'09},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {5710},
  pages =               {196-210},
  year =                {2009},
  month =               sep,
  doi =                 {10.1007/978-3-642-04081-8_14},
  abstract =            {In this paper, we extend the classical notion of
                         strategies in turn-based finite games by allowing
                         several moves to be selected. We~define and study a
                         quantitative measure for permissivity of such
                         strategies by assigning penalties when blocking
                         transitions. We~prove that for reachability
                         objectives, most permissive strategies exist, can be
                         chosen memoryless, and can be computed in polynomial
                         time, while it is in
                         \(\textsf{NP}\cap\textsf{coNP}\) for discounted and
                         mean penalties.},
}

@inproceedings{stacs2003-BDR,
  author =              {Bruy{\`e}re, V{\'e}ronique and Dall'Olio, Emmanuel
                         and Raskin, Jean-Fran{\c c}ois},
  title =               {Durations, Parametric Model Checking in Timed
                         Automata with {P}resburger Arithmetic},
  editor =              {Alt, Helmut and Habib, Michel},
  booktitle =           {{P}roceedings of the 20th {S}ymposium on
                         {T}heoretical {A}spects of {C}omputer {S}cience
                         ({STACS}'03)},
  acronym =             {{STACS}'03},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2607},
  pages =               {687-698},
  year =                {2003},
  month =               feb,
}

@article{deds19(2)-BDSD,
  author =              {Bherer, Hans and Desharnais, Jules and St-Denis,
                         Richard},
  title =               {Control of Parameterized Discrete Event Systems},
  publisher =           {Kluwer Academic},
  journal =             {Discrete Event Dynamic Systems},
  volume =              {19},
  number =              {2},
  pages =               {213-165},
  year =                {2009},
  month =               jun,
  doi =                 {10.1007/s10626-008-0040-9},
}

@article{tcs292(1)-Bea,
  author =              {Beauquier, Dani{\`e}le},
  title =               {On~probabilistic timed automata},
  publisher =           {Elsevier},
  journal =             {Theoretical Computer Science},
  volume =              {292},
  number =              {1},
  pages =               {65-84},
  year =                {2003},
  month =               jan,
  doi =                 {10.1016/S0304-3975(01)00215-8},
}

@article{jcss63(3)-Bed,
  author =              {Bedon, Nicolas},
  title =               {Logic over Words on Denumerable Ordinals},
  publisher =           {Academic Press},
  journal =             {Journal of Computer and System Sciences},
  volume =              {63},
  number =              {3},
  pages =               {394-431},
  year =                {2001},
  month =               nov,
}

@inproceedings{stacs2015-BEGM,
  author =              {Boros, Endre and Elbassioni, Khaled and Gurvich,
                         Vladimir and Makino, Kazuhisa},
  title =               {{M}arkov Decision Processes and Stochastic Games
                         with Total Effective Payoff},
  editor =              {Mayr, Ernst W. and Ollinger, Nicolas},
  booktitle =           {{P}roceedings of the 32nd {S}ymposium on
                         {T}heoretical {A}spects of {C}omputer {S}cience
                         ({STACS}'15)},
  acronym =             {{STACS}'15},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {30},
  pages =               {103-115},
  year =                {2015},
  month =               mar,
  doi =                 {10.4230/LIPIcs.STACS.2015.103},
}

@article{tcs84(2)-Bei,
  author =              {Beigel, Richard},
  title =               {Bounded Queries to {SAT} and the {B}oolean
                         Hierarchy},
  publisher =           {Elsevier},
  journal =             {Theoretical Computer Science},
  volume =              {84},
  number =              {2},
  pages =               {199-223},
  year =                {1991},
}

@inproceedings{concur2018-BEK,
  author =              {Blondin, Michael and Esparza, Javier and Ku{\v
                         c}era, Anton{\'\i}n},
  title =               {Automatic Analysis of Expected Termination Time for
                         Population Protocols},
  editor =              {Schewe, Sven and Zhang, Lijun},
  booktitle =           {{P}roceedings of the 29th {I}nternational
                         {C}onference on {C}oncurrency {T}heory
                         ({CONCUR}'18)},
  acronym =             {{CONCUR}'18},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {118},
  pages =               {33:1-33:16},
  year =                {2018},
  month =               sep,
  doi =                 {10.4230/LIPIcs.CONCUR.2018.33},
}

@book{DP-Bel,
  author =              {Bellman, Richard},
  title =               {Dynamic Programming},
  publisher =           {Princeton University Press},
  year =                {1957},
}

@article{qam16(1)-Bel,
  author =              {Bellman, Richard},
  title =               {On a Routing Problem},
  journal =             {Quarterly of Applied Mathematics},
  volume =              {16},
  number =              {1},
  pages =               {87-90},
  year =                {1958},
}

@phdthesis{phd-belmokadem,
  author =              {Bel{~}Mokadem, Houda},
  title =               {V{\'e}rification des propri{\'e}t{\'e}s
                         temporis{\'e}es des automates programmables
                         industriels},
  year =                {2006},
  month =               sep,
  school =              {Lab.~Sp\'ecification \& V\'erification, ENS Cachan,
                         France},
  type =                {Th\`ese de doctorat},
}

@inproceedings{icalp1996-BEM,
  author =              {Bradfield, Julian C. and Esparza, Javier and Mader,
                         Angelika},
  title =               {An effective tableau system for the linear time
                         mu-calculus},
  editor =              {Meyer auf der Heide, Friedhelm and Monien, Burkhard},
  booktitle =           {{P}roceedings of the 23rd {I}nternational
                         {C}olloquium on {A}utomata, {L}anguages and
                         {P}rogramming ({ICALP}'96)},
  acronym =             {{ICALP}'96},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {1099},
  pages =               {98-109},
  year =                {1996},
  month =               jul,
}

@incollection{PLI2000-Ber,
  author =              {Berry, G{\'e}rard},
  title =               {The foundations of {E}sterel},
  editor =              {Plotkin, Gordon D. and Stirling, Colin and Tofte,
                         Mads},
  booktitle =           {Proof, Language, and Interaction~-- Essays in Honour
                         of {R}obin {M}ilner},
  publisher =           {MIT Press},
  pages =               {425-454},
  year =                {2000},
}

@inproceedings{rttools2001-Bey,
  author =              {Beyer, Dirk},
  title =               {Rabbit: Verification of Real-Time Systems},
  editor =              {Pettersson, Paul and Yovine, Sergio},
  booktitle =           {{P}roceedings of the 1st {W}orkshop on {R}eal-Time
                         {T}ools ({RT-TOOLS}'01)},
  acronym =             {{RT-TOOLS}'01},
  pages =               {13-21},
  year =                {2001},
  month =               aug,
}

@inproceedings{icalp2009-BF,
  author =              {Bouyer, Patricia and Forejt, Vojt{\v{e}}ch},
  title =               {Reachability in Stochastic Timed Games},
  editor =              {Albers, Susanne and Marchetti{-}Spaccamela Alberto
                         and Matias, Yossi and Nikoletseas, Sotiris and
                         Thomas, Wolfgang},
  booktitle =           {{P}roceedings of the 36th {I}nternational
                         {C}olloquium on {A}utomata, {L}anguages and
                         {P}rogramming ({ICALP}'09)~-- Part~{II}},
  acronym =             {{ICALP}'09},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {5556},
  pages =               {103-114},
  year =                {2009},
  month =               jul,
}

@book{lectRV-BF18,
  title =               {Lectures on Runtime Verification},
  editor =              {Bartocci, Ezio and Falcone, Yli{\`e}s},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {10457},
  year =                {2018},
  doi =                 {10.1007/978-3-319-75632-5},
}

@article{geb92()-BFA,
  author =              {Bhaskar, Umang and Fleischer, Lisa and Anshelevich,
                         Elliot},
  title =               {A~{S}tackelberg strategy for routing flow over time},
  journal =             {Games and Economic Behavior},
  volume =              {92},
  pages =               {232-247},
  year =                {2015},
  month =               jul,
  doi =                 {10.1016/j.geb.2013.09.004},
}

@article{jlc12(4)-BFD,
  author =              {Bolotov, Alexander and Fischer, Michael J. and
                         Dixon, Clare},
  title =               {On the Relationship between {\(\omega\)}-Automata
                         and Temporal Logic Normal Forms},
  publisher =           {Oxford University Press},
  journal =             {Journal of Logic and Computation},
  volume =              {12},
  number =              {4},
  pages =               {561-581},
  year =                {2002},
  month =               aug,
}

@techreport{arxiv2002.03664-BFFGMMPPRS,
  author =              {Berthon, Rapha{\"e}l and Fijalkow, Nathana{\"e}l and
                         Filiot, Emmanuel and Guha, Shibashis and Maubert,
                         Bastien and Murano, Aniello and Pinault, Laureline
                         and Pinchinat, Sophie and Rubin, Sasha and Serre,
                         Olivier},
  title =               {Alternating Tree Automata with Qualitative
                         Semantics},
  number =              {2002-03664},
  year =                {2020},
  month =               feb,
  institution =         {arXiv},
}

@article{tocl22(1)-BFFGMMPPRS,
  author =              {Berthon, Rapha{\"e}l and Fijalkow, Nathana{\"e}l and
                         Filiot, Emmanuel and Guha, Shibashis and Maubert,
                         Bastien and Murano, Aniello and Pinault, Laureline
                         and Pinchinat, Sophie and Rubin, Sasha and Serre,
                         Olivier},
  title =               {Alternating Tree Automata with Qualitative
                         Semantics},
  publisher =           {ACM Press},
  journal =             {ACM Transactions on Computational Logic},
  volume =              {22},
  number =              {1},
  pages =               {7:1-7:24},
  year =                {2021},
  month =               jan,
  doi =                 {10.1145/3431860},
}

@article{alga61(2)-BFFM,
  author =              {Bil{\`o}, Vittorio and Fanelli, Angelo and Flammini,
                         Michele and Moscardelli, Luca},
  title =               {Graphical congestion games},
  publisher =           {Springer-Verlag},
  journal =             {Algorithmica},
  volume =              {61},
  number =              {2},
  pages =               {274-297},
  year =                {2011},
  month =               oct,
  doi =                 {10.1007/s00453-010-9417-x},
}

@article{jcss75(3)-BFH,
  author =              {Brandt, Felix and Fischer, Felix and Holzer, Markus},
  title =               {Symmetries and the complexity of pure {N}ash
                         equilibrium},
  publisher =           {Elsevier},
  journal =             {Journal of Computer and System Sciences},
  volume =              {75},
  number =              {3},
  pages =               {163-177},
  year =                {2009},
  month =               may,
}

@article{tac48(5)-BFHJ,
  author =              {Benveniste, Albert and Fabre, {\'E}ric and Haar,
                         Stefan and Jard, Claude},
  title =               {Diagnosis of asynchronous discrete event systems:
                         A~net-unfolding approach},
  publisher =           {IEEE Comp. Soc. Press},
  journal =             {IEEE Transactions on Automatic Control},
  volume =              {48},
  number =              {5},
  pages =               {714-727},
  year =                {2003},
  doi =                 {10.1109/TAC.2003.811249},
}

@inproceedings{tacas2001-BFHLPR,
  author =              {Behrmann, Gerd and Fehnker, Ansgar and Hune, Thomas
                         and Larsen, Kim Guldstrand and Pettersson, Paul and
                         Romijn, Judi},
  title =               {Efficient Guiding Towards Cost-Optimality in UPPAAL},
  editor =              {Margaria, Tiziana and Yi, Wang},
  booktitle =           {{P}roceedings of the 7th {I}nternational
                         {C}onference on {T}ools and {A}lgorithms for
                         {C}onstruction and {A}nalysis of {S}ystems
                         ({TACAS}'01)},
  acronym =             {{TACAS}'01},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2031},
  pages =               {174-188},
  year =                {2001},
  month =               apr,
}

@inproceedings{hscc2001-BFHLPRV,
  author =              {Behrmann, Gerd and Fehnker, Ansgar and Hune, Thomas
                         and Larsen, Kim Guldstrand and Pettersson, Paul and
                         Romijn, Judi and Vaandrager, Frits},
  title =               {Minimum-Cost Reachability for Priced Timed Automata},
  editor =              {Di{~}Benedetto, Maria Domenica and
                         Sangiovani{-}Vincentelli, Alberto L.},
  booktitle =           {{P}roceedings of the 4th {I}nternational {W}orkshop
                         on {H}ybrid {S}ystems: {C}omputation and {C}ontrol
                         ({HSCC}'01)},
  acronym =             {{HSCC}'01},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2034},
  pages =               {147-161},
  year =                {2001},
  month =               mar,
  doi =                 {10.1007/3-540-45351-2_15},
}

Abstract

In this paper, we study one-clock priced timed automata in which prices can grow linearly (dp/dt=k) or exponentially (dp/dt=kp), with discontinuous updates on edges. We propose EXPTIME algorithms to decide the existence of controllers that ensure existence of infinite runs or reachability of some goal location with non-negative observer value all along the run. These algorithms consist in computing the optimal delays that should be elapsed in each location along a run, so that the final observer value is maximized (and never goes below zero).

@inproceedings{hscc2010-BFLM,
  author =              {Bouyer, Patricia and Fahrenberg, Uli and Larsen, Kim
                         Guldstrand and Markey, Nicolas},
  title =               {Timed Automata with Observers under Energy
                         Constraints},
  editor =              {Johansson, Karl Henrik and Yi, Wang},
  booktitle =           {{P}roceedings of the 13th {I}nternational {W}orkshop
                         on {H}ybrid {S}ystems: {C}omputation and {C}ontrol
                         ({HSCC}'10)},
  acronym =             {{HSCC}'10},
  publisher =           {ACM Press},
  pages =               {61-70},
  year =                {2010},
  month =               apr,
  doi =                 {10.1145/1755952.1755963},
  abstract =            {In this paper, we study one-clock priced timed
                         automata in which prices can grow linearly
                         (\(\frac{dp}{dt}=k\)) or exponentially
                         (\(\frac{dp}{dt}=kp\)), with discontinuous updates
                         on edges. We propose EXPTIME algorithms to decide
                         the existence of controllers that ensure existence
                         of infinite runs or reachability of some goal
                         location with non-negative observer value all along
                         the run. These algorithms consist in computing the
                         optimal delays that should be elapsed in each
                         location along a run, so that the final observer
                         value is maximized (and never goes below zero).},
}

Abstract

The problems of time-dependent behavior in general, and dynamic resource allocation in particular, pervade many aspects of modern life. Prominent examples range from reliability and efficient use of communication resources in a telecommunication network to the allocation of tracks in a continental railway network, from scheduling the usage of computational resources on a chip for durations of nano-seconds to the weekly, monthly, or longer-range reactive planning in a factory or a supply chain.

@article{cacm54(9)-BFLM,
  author =              {Bouyer, Patricia and Fahrenberg, Uli and Larsen, Kim
                         Guldstrand and Markey, Nicolas},
  title =               {Quantitative analysis of real-time systems using
                         priced timed automata},
  publisher =           {ACM Press},
  journal =             {Communications of the ACM},
  volume =              {54},
  number =              {9},
  pages =               {78-87},
  year =                {2011},
  month =               sep,
  doi =                 {10.1145/1995376.1995396},
  abstract =            {The problems of time-dependent behavior in general,
                         and dynamic resource allocation in particular,
                         pervade many aspects of modern life. Prominent
                         examples range from reliability and efficient use of
                         communication resources in a telecommunication
                         network to the allocation of tracks in a continental
                         railway network, from scheduling the usage of
                         computational resources on a chip for durations of
                         nano-seconds to the weekly, monthly, or longer-range
                         reactive planning in a factory or a supply chain.},
}

Abstract

This chapter surveys timed automata as a formalism for model checking real-time systems. We begin with introducing the model, as an extension of finite-state automata with real-valued variables for measuring time. We then present the main model-checking results in this framework, and give a hint about some recent extensions (namely weighted timed automata and timed games).

@incollection{hmc2018-BFLMOW,
  author =              {Bouyer, Patricia and Fahrenberg, Uli and Larsen, Kim
                         Guldstrand and Markey, Nicolas and Ouaknine,
                         Jo{\"e}l and Worrell, James},
  title =               {Model Checking Real-Time Systems},
  editor =              {Clarke, Edmund M. and Henzinger, Thomas A. and
                         Veith, Helmut and Bloem, Roderick},
  booktitle =           {Handbook of Model Checking},
  publisher =           {Springer-Verlag},
  pages =               {1001-1046},
  chapter =             {29},
  year =                {2018},
  month =               may,
  doi =                 {10.1007/978-3-319-10575-8_29},
  abstract =            {This chapter surveys timed automata as a formalism
                         for model checking real-time systems. We begin with
                         introducing the model, as an extension of
                         finite-state automata with real-valued variables for
                         measuring time. We then present the main
                         model-checking results in this framework, and give a
                         hint about some recent extensions (namely weighted
                         timed automata and timed games).},
}

Abstract

We study the problems of existence and construction of infinite schedules for finite weighted automata and one-clock weighted timed automata, subject to boundary constraints on the accumulated weight. More specifically, we consider automata equipped with positive and negative weights on transitions and locations, corresponding to the production and consumption of some resource (e.g. energy). We ask the question whether there exists an infinite path for which the accumulated weight for any finite prefix satisfies certain constraints (e.g. remains between 0 and some given upper-bound). We also consider a game version of the above, where certain transitions may be uncontrollable.

@inproceedings{formats2008-BFLMS,
  author =              {Bouyer, Patricia and Fahrenberg, Uli and Larsen, Kim
                         Guldstrand and Markey, Nicolas and Srba, Ji{\v
                         r}{\'\i}},
  title =               {Infinite Runs in Weighted Timed Automata with Energy
                         Constraints},
  editor =              {Cassez, Franck and Jard, Claude},
  booktitle =           {{P}roceedings of the 6th {I}nternational
                         {C}onferences on {F}ormal {M}odelling and {A}nalysis
                         of {T}imed {S}ystems ({FORMATS}'08)},
  acronym =             {{FORMATS}'08},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {5215},
  pages =               {33-47},
  year =                {2008},
  month =               sep,
  doi =                 {10.1007/978-3-540-85778-5_4},
  abstract =            {We~study the problems of existence and construction
                         of infinite schedules for finite weighted automata
                         and one-clock weighted timed automata, subject to
                         boundary constraints on the accumulated weight. More
                         specifically, we~consider automata equipped with
                         positive and negative weights on transitions and
                         locations, corresponding to the production and
                         consumption of some resource (\emph{e.g.}~energy).
                         We~ask the question whether there exists an infinite
                         path for which the accumulated weight for any finite
                         prefix satisfies certain constraints
                         (\emph{e.g.}~remains between~\(0\) and some given
                         upper-bound). We~also consider a game version of the
                         above, where certain transitions may be
                         uncontrollable.},
}

Abstract

Timed automata are a convenient framework for modelling and reasoning about real-time systems. While these models are now very well-understood, they do not offer a convenient way of taking timing imprecisions into account. Several solutions (e.g. parametric guard enlargement) have recently been proposed over the last ten years to take such imprecisions into account. In this paper, we propose a new approach for handling robust reachability, based on permissive strategies. While classical strategies propose to play an action at an exact point in time, permissive strategies return an interval of possible dates when to play the selected action. With such a permissive strategy, we associate a penalty, which is the inverse of the length of the proposed interval, and accumulates along the run. We show that in that setting, optimal strategies can be computed in polynomial time for one-clock timed automata.

@inproceedings{avocs2015-BFM,
  author =              {Bouyer, Patricia and Fang, Erwin and Markey,
                         Nicolas},
  title =               {Permissive strategies in timed automata and games},
  editor =              {Grov, Gudmund and Ireland, Andrew},
  booktitle =           {{P}roceedings of the 15th {I}nternational {W}orkshop
                         on {A}utomated {V}erification of {C}ritical
                         {S}ystems ({AVOCS}'15)},
  acronym =             {{AVOCS}'15},
  publisher =           {European Association of Software Science and
                         Technology},
  series =              {Electronic Communications of the EASST},
  volume =              {72},
  year =                {2015},
  month =               sep,
  doi =                 {10.14279/tuj.eceasst.72.1015},
  abstract =            {Timed automata are a convenient framework for
                         modelling and reasoning about real-time systems.
                         While these models are now very well-understood,
                         they do not offer a convenient way of taking timing
                         imprecisions into account. Several solutions (e.g.
                         parametric guard enlargement) have recently been
                         proposed over the last ten years to take such
                         imprecisions into account. In this paper, we propose
                         a new approach for handling robust reachability,
                         based on permissive strategies. While classical
                         strategies propose to play an action at an exact
                         point in time, permissive strategies return an
                         interval of possible dates when to play the selected
                         action. With such a permissive strategy, we
                         associate a penalty, which is the inverse of the
                         length of the proposed interval, and accumulates
                         along the run. We show that in that setting, optimal
                         strategies can be computed in polynomial time for
                         one-clock timed automata.},
}

Abstract

Synchronizing a (deterministic, finite-state) automaton is the problem of finding a sequence of actions to be played in the automaton in order to end up in the same state independently of the starting state. We consider synchronization with LTL constraints on the executions leading to synchronization, extending the results of [Petra Wolf. Synchronization under dynamic constraints. FSTTCS'20] by showing that the problem is PSPACE-complete for LTL as well as for restricted fragments (involving only modality F or G), while it is NP-complete for constraints expressed using only modality X.

@article{ipl182()-BFM,
  author =              {Bertrand, Nathalie and Francon, Hugo and Markey,
                         Nicolas},
  title =               {Synchronizing words under {LTL} constraints},
  publisher =           {Elsevier},
  journal =             {Information Processing Letters},
  volume =              {182},
  year =                {2023},
  month =               aug,
  doi =                 {10.1016/j.ipl.2023.106392},
  abstract =            {Synchronizing a (deterministic, finite-state)
                         automaton is the problem of finding a sequence of
                         actions to be played in the automaton in order to
                         end up in the same state independently of the
                         starting state. We~consider synchronization
                         with~\textsf{LTL} constraints on the executions
                         leading to synchronization, extending the results
                         of~[Petra~Wolf. Synchronization under dynamic
                         constraints. FSTTCS'20] by~showing that the problem
                         is \textsf{PSPACE}-complete for~\textsf{LTL} as well
                         as for restricted fragments (involving only
                         modality~\textsf{F} or~\textsf{G}), while it is
                         \textsf{NP}-complete for constraints expressed using
                         only modality~\textsf{X}.},
}

@article{jcss7(4)-BFPRT,
  author =              {Blum, Manuel and Floyd, Robert W. and Pratt, Vaughan
                         R. and Rivest, Ronald L. and Tarjan, Robert Endre},
  title =               {Time Bounds for Selection},
  publisher =           {Academic Press},
  journal =             {Journal of Computer and System Sciences},
  volume =              {7},
  number =              {4},
  pages =               {448-461},
  year =                {1973},
  month =               aug,
}

@inproceedings{fossacs2014-BFS,
  author =              {Bertrand, Nathalie and Fournier, Paulin and
                         Sangnier, Arnaud},
  title =               {Playing with Probabilities in Reconfigurable
                         Broadcast Networks},
  editor =              {Muscholl, Anca},
  booktitle =           {{P}roceedings of the 17th {I}nternational
                         {C}onference on {F}oundations of {S}oftware
                         {S}cience and {C}omputation {S}tructure
                         ({FoSSaCS}'14)},
  acronym =             {{FoSSaCS}'14},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {8412},
  pages =               {134-148},
  year =                {2014},
  month =               apr,
  doi =                 {10.1007/978-3-642-54830-7_9},
}

@inproceedings{concur2015-BFS,
  author =              {Bertrand, Nathalie and Fournier, Paulin and
                         Sangnier, Arnaud},
  title =               {Distributed Local Strategies in Broadcast Networks},
  editor =              {Aceto, Luca and de Frutos{-}Escrig, David},
  booktitle =           {{P}roceedings of the 26th {I}nternational
                         {C}onference on {C}oncurrency {T}heory
                         ({CONCUR}'15)},
  acronym =             {{CONCUR}'15},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {42},
  pages =               {44-57},
  year =                {2015},
  month =               sep,
  doi =                 {10.4230/LIPIcs.CONCUR.2015.44},
}

@article{ndjfl26(2)-BG,
  author =              {Burgess,John P. and Gurevich, Yuri},
  title =               {The Decision Problem for Linear Temporal Logic},
  journal =             {Notre Dame Journal of Formal Logic},
  volume =              {26},
  number =              {2},
  pages =               {115-128},
  year =                {1985},
  month =               apr,
}

@inproceedings{concur1993-BG,
  author =              {Bernholtz, Orna and Grumberg, Orna},
  title =               {Branching Time Temporal Logic and {{\(\mathcal{A}
                         \textup{m} \textbf{o} r \textsc{p} \mathcal{H}
                         \texttt{O} u \textbf{s}\)}} Tree Automata},
  editor =              {Best, Eike},
  booktitle =           {{P}roceedings of the 4th {I}nternational
                         {C}onference on {C}oncurrency {T}heory
                         ({CONCUR}'93)},
  acronym =             {{CONCUR}'93},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {715},
  pages =               {262-277},
  year =                {1993},
  month =               aug,
}

@inproceedings{cav1999-BG,
  author =              {Bruns, Glenn and Godefroid, Patrice},
  title =               {Model Checking Partial State Spaces with
                         {\(3\)}-Valued Temporal Logics},
  editor =              {Halbwachs, Nicolas and Peled, Doron A.},
  booktitle =           {{P}roceedings of the 11th {I}nternational
                         {C}onference on {C}omputer {A}ided {V}erification
                         ({CAV}'99)},
  acronym =             {{CAV}'99},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {1633},
  pages =               {274-287},
  year =                {1999},
  month =               jul,
}

@inproceedings{lics2001-BG,
  author =              {Bruns, Glenn and Godefroid, Patrice},
  title =               {Temporal Logic Query Checking (Extended Abstract)},
  booktitle =           {{P}roceedings of the 16th {A}nnual {S}ymposium on
                         {L}ogic in {C}omputer {S}cience ({LICS}'01)},
  acronym =             {{LICS}'01},
  publisher =           {IEEE Comp. Soc. Press},
  pages =               {409-417},
  year =                {2001},
  month =               jun,
}

@article{tcs289(1)-BG,
  author =              {Baumgartner, Robert and Gottlob, Georg},
  title =               {Propositional Default Logics made Easier:
                         Computational Complexity of Model Checking},
  publisher =           {Elsevier},
  journal =             {Theoretical Computer Science},
  volume =              {289},
  number =              {1},
  pages =               {591-627},
  year =                {2002},
  month =               oct,
}

@inproceedings{stacs2004-BG,
  author =              {Barbanchon, R{\'e}gis and Grandjean, {\'E}tienne},
  title =               {The Minimal Logically-Defined {NP}-Complete Problem},
  editor =              {Diekert, Volker and Habib, Michel},
  booktitle =           {{P}roceedings of the 21st {S}ymposium on
                         {T}heoretical {A}spects of {C}omputer {S}cience
                         ({STACS}'04)},
  acronym =             {{STACS}'04},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2996},
  pages =               {338-349},
  year =                {2003},
  month =               mar,
}

@article{TCSyst37(6)-BG,
  author =              {Berwanger, Dietmar and Gr{\"a}del, Erich},
  title =               {Fixed-Point Logics and Solitaire Games},
  publisher =           {Springer-Verlag},
  journal =             {Theory of Computing Systems},
  volume =              {37},
  number =              {6},
  pages =               {675-694},
  year =                {2004},
  month =               dec,
  doi =                 {10.1007/s00224-004-1147-5},
}

@inproceedings{lpar2004-BG,
  author =              {Berwanger, Dietmar and Gr{\"a}del, Erich},
  title =               {Entanglement~-- {A}~Measure for the Complexity of
                         Directed Graphs with Applications to Logic and
                         Games},
  editor =              {Baader, Franz and Voronkov, Andrei},
  booktitle =           {{P}roceedings of the 11th {I}nternational
                         {C}onference {L}ogic {P}rogramming and {A}utomated
                         {R}easoning ({LPAR}'04)},
  acronym =             {{LPAR}'04},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {3452},
  pages =               {209-223},
  year =                {2005},
  month =               mar,
}

@inproceedings{fsttcs2011-BG,
  author =              {Bertrand, Nathalie and Genest, Blaise},
  title =               {Minimal Disclosure in {P}artially {O}bservable
                         {M}arkov {D}ecision {P}rocesses},
  editor =              {Chakraborty, Supratik and Kumar, Amit},
  booktitle =           {{P}roceedings of the 31st {C}onference on
                         {F}oundations of {S}oftware {T}echnology and
                         {T}heoretical {C}omputer {S}cience ({FSTTCS}'11)},
  acronym =             {{FSTTCS}'11},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {13},
  pages =               {411-422},
  year =                {2011},
  month =               dec,
  doi =                 {10.4230/LIPIcs.FSTTCS.2011.411},
}

@inproceedings{sr2013-BG,
  author =              {Bulling, Nils and Goranko, Valentin},
  title =               {How to Be Both Rich and Happy: Combining
                         Quantitative and Qualitative Strategic Reasoning
                         about Multi-Player Games (Extended Abstract)},
  booktitle =           {{P}roceedings of the 1st {I}nternational {W}orkshop
                         on {S}trategic {R}easoning ({SR}'13)},
  acronym =             {{SR}'13},
  series =              {Electronic Proceedings in Theoretical Computer
                         Science},
  volume =              {112},
  pages =               {33-41},
  year =                {2013},
  month =               mar,
  doi =                 {10.4204/EPTCS.112.8},
}

@article{jacm64(5)-BGG,
  author =              {Bertrand, Nathalie and Genest, Blaise and Gimbert,
                         Hugo},
  title =               {Qualitative Determinacy and Decidability of
                         Stochastic Games with Signals},
  publisher =           {ACM Press},
  journal =             {Journal of the~ACM},
  volume =              {64},
  number =              {5},
  pages =               {33:1-33:48},
  year =                {2017},
  month =               oct,
  doi =                 {10.1145/3107926},
}

@article{jcss79(5)-BGH,
  author =              {Bournez, Olivier and Gra{\c c}a, Daniel S. and
                         Hainry, Emmanuel},
  title =               {Computation with perturbed dynamical systems},
  publisher =           {Elsevier},
  journal =             {Journal of Computer and System Sciences},
  volume =              {79},
  number =              {5},
  pages =               {714-724},
  year =                {2013},
  month =               aug,
}

@inproceedings{fmcad2009-BGHJ,
  author =              {Bloem, Roderick and Greimel, Karin and Henzinger,
                         Thomas A. and Jobstmann, Barbara},
  title =               {Synthesizing robust systems},
  booktitle =           {{P}roceedings of the 9th {I}nternational
                         {C}onference on {F}ormal {M}ethods in
                         {C}omputer-{A}ided {D}esign ({FMCAD}'09)},
  acronym =             {{FMCAD}'09},
  publisher =           {IEEE Comp. Soc. Press},
  pages =               {85-92},
  year =                {2009},
  month =               nov,
}

@inproceedings{fsttcs2005-BGHLM,
  author =              {Brihaye, {\relax Th}omas and Geeraerts, Gilles and
                         Haddad, Axel and Lefaucheux, Engel and Monmege,
                         Benjamin},
  title =               {Simple priced timed games are not that simple},
  editor =              {Harsha, Prahladh and Ramalingam, G.},
  booktitle =           {{P}roceedings of the 35th {C}onference on
                         {F}oundations of {S}oftware {T}echnology and
                         {T}heoretical {C}omputer {S}cience ({FSTTCS}'15)},
  acronym =             {{FSTTCS}'15},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {45},
  pages =               {278-292},
  year =                {2015},
  month =               dec,
  doi =                 {10.4230/LIPIcs.FSTTCS.2015.278},
}

@article{acta54(1)-BGHM,
  author =              {Brihaye, {\relax Th}omas and Geeraerts, Gilles and
                         Haddad, Axel and Monmege, Benjamin},
  title =               {Pseudopolynomial iterative algorithm to solve
                         total-payoff games and min-cost reachability game},
  publisher =           {Springer-Verlag},
  journal =             {Acta Informatica},
  volume =              {54},
  number =              {1},
  pages =               {85-125},
  year =                {2017},
  month =               feb,
  doi =                 {10.1007/s00236-016-0276-z},
}

@inproceedings{crypto2001-BGIRSVY,
  author =              {Barak, Boaz and Goldreich, Oded and Impagliazzo,
                         Rusell and Rudich, Steven and Sahai, Amit and
                         Vadhan, Salil and Yang, Ke},
  title =               {On the (Im)possibility of Obfuscating Programs},
  editor =              {Kilian, Joe},
  booktitle =           {{P}roceedings of the 21st {A}nnual {I}nternational
                         {C}ryptology {C}onference ({CRYPTO}'01)},
  acronym =             {{CRYPTO}'01},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {2139},
  pages =               {1-18},
  year =                {2001},
  month =               aug,
}

@techreport{eccc2001-BGIRSVY,
  author =              {Barak, Boaz and Goldreich, Oded and Impagliazzo,
                         Rusell and Rudich, Steven and Sahai, Amit and
                         Vadhan, Salil and Yang, Ke},
  title =               {On the (Im)possibility of Obfuscating Programs},
  number =              {01-057},
  year =                {2001},
  month =               aug,
  institution =         {Electronic Colloquium on Computational Complexity},
  type =                {Research Report},
}

@inproceedings{cav1996-BGKLLPY,
  author =              {Bengtsson, Johan and Griffioen, W. O. David and
                         Kristoffersen, K{\aa}re J. and Larsen, Kim
                         Guldstrand and Larsson, Fredrik and Pettersson, Paul
                         and Yi, Wang},
  title =               {Verification of an Audio Protocol with Bus Collision
                         Using {\scshape {U}ppaal}},
  editor =              {Alur, Rajeev and Henzinger, Thomas A.},
  booktitle =           {{P}roceedings of the 8th {I}nternational
                         {C}onference on {C}omputer {A}ided {V}erification
                         ({CAV}'96)},
  acronym =             {{CAV}'96},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {1102},
  pages =               {244-256},
  year =                {1996},
  month =               jul,
}

Abstract

Extending formal verification techniques to handle quantitative aspects, both for the models and for the properties to be checked, has become a central research topic over the last twenty years. Following several recent works, we study model checking for (one-dimensional) weighted Kripke structures with positive and negative weights, and temporal logics constraining the total and/or average weight. We prove decidability when only accumulated weight is constrained, while allowing average-weight constraints alone already is undecidable.

@inproceedings{atva2014-BGM,
  author =              {Bouyer, Patricia and Gardy, Patrick and Markey,
                         Nicolas},
  title =               {Quantitative verification of weighted {K}ripke
                         structures},
  editor =              {Cassez, Franck and Raskin, Jean-Fran{\c c}ois},
  booktitle =           {{P}roceedings of the 12th {I}nternational
                         {S}ymposium on {A}utomated {T}echnology for
                         {V}erification and {A}nalysis ({ATVA}'14)},
  acronym =             {{ATVA}'14},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {8837},
  pages =               {64-80},
  year =                {2014},
  month =               nov,
  doi =                 {10.1007/978-3-319-11936-6_6},
  abstract =            {Extending formal verification techniques to handle
                         quantitative aspects, both for the models and for
                         the properties to be checked, has become a central
                         research topic over the last twenty years. Following
                         several recent works, we study model checking for
                         (one-dimensional) weighted Kripke structures with
                         positive and negative weights, and temporal logics
                         constraining the total and/or average weight. We
                         prove decidability when only accumulated weight is
                         constrained, while allowing average-weight
                         constraints alone already is undecidable.},
}

Abstract

Strategy Logic is a powerful specification language for expressing non-zero-sum properties of multi-player games. SL conveniently extends the logic ATL with explicit quantification and assignment of strategies. In this paper, we consider games over one-counter automata, and a quantitative extension 1cSL of SL with assertions over the value of the counter. We prove two results: we first show that, if decidable, model checking the so-called Boolean-goal fragment of 1cSL has non-elementary complexity; we actually prove the result for the Boolean-goal fragment of SL over finite-state games, which was an open question in (Mogavero et al. Reasoning about strategies: On the model-checking problem. 2014). As a first step towards proving decidability, we then show that the Boolean-goal fragment of 1cSL over one-counter games enjoys a nice periodicity property.

@inproceedings{fsttcs2015-BGM,
  author =              {Bouyer, Patricia and Gardy, Patrick and Markey,
                         Nicolas},
  title =               {Weighted strategy logic with boolean goals over
                         one-counter games},
  editor =              {Harsha, Prahladh and Ramalingam, G.},
  booktitle =           {{P}roceedings of the 35th {C}onference on
                         {F}oundations of {S}oftware {T}echnology and
                         {T}heoretical {C}omputer {S}cience ({FSTTCS}'15)},
  acronym =             {{FSTTCS}'15},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {45},
  pages =               {69-83},
  year =                {2015},
  month =               dec,
  doi =                 {10.4230/LIPIcs.FSTTCS.2015.69},
  abstract =            {Strategy Logic is a powerful specification language
                         for expressing non-zero-sum properties of
                         multi-player games. SL conveniently extends the
                         logic ATL with explicit quantification and
                         assignment of strategies. In this paper, we consider
                         games over one-counter automata, and a quantitative
                         extension 1cSL of SL with assertions over the value
                         of the counter. We prove two results: we first show
                         that, if decidable, model checking the so-called
                         Boolean-goal fragment of 1cSL has non-elementary
                         complexity; we actually prove the result for the
                         Boolean-goal fragment of SL over finite-state games,
                         which was an open question in (Mogavero
                         \emph{et~al.} Reasoning about strategies: On the
                         model-checking problem. 2014). As a first step
                         towards proving decidability, we then show that the
                         Boolean-goal fragment of 1cSL over one-counter games
                         enjoys a nice periodicity property.},
}

Abstract

We define and study a slight variation on the semantics of Strategy Logic: while in the classical semantics, all strategies are shifted during the evaluation of temporal modalities, we propose to only shift the strategies that have been assigned to a player, thus matching the intuition that we can assign the very same strategy to the players at different points in time. We prove that surprisingly, this renders the model-checking problem undecidable.