Nicolas Markey

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.},
}

Abstract

Reachability checking is one of the most basic problems in verification. By solving this problem in a game, one can synthesize a strategy that dictates the actions to be performed for ensuring that the target location is reached. In this work, we are interested in synthesizing "robust" strategies for ensuring reachability of a location in timed automata. By robust, we mean that it must still ensure reachability even when the delays are perturbed by the environment. We model this perturbed semantics as a game between the controller and its environment, and solve the parameterized robust reachability problem: we show that the existence of an upper bound on the perturbations under which there is a strategy reaching a target location is EXPTIME-complete. We also extend our algorithm, with the same complexity, to turn-based timed games, where the successor state is entirely determined by the environment in some locations.

@article{tcs563()-BMS,
  author =              {Bouyer, Patricia and Markey, Nicolas and Sankur,
                         Ocan},
  title =               {Robust Reachability in Timed Automata and Games:
                         A~Game-based Approach},
  publisher =           {Elsevier},
  journal =             {Theoretical Computer Science},
  volume =              {563},
  pages =               {43-74},
  year =                {2015},
  month =               jan,
  doi =                 {10.1016/j.tcs.2014.08.014},
  abstract =            {Reachability checking is one of the most basic
                         problems in verification. By solving this problem in
                         a game, one can synthesize a strategy that dictates
                         the actions to be performed for ensuring that the
                         target location is reached. In this work, we are
                         interested in synthesizing {"}robust{"} strategies
                         for ensuring reachability of a location in timed
                         automata. By robust, we mean that it must still
                         ensure reachability even when the delays are
                         perturbed by the environment. We model this
                         perturbed semantics as a game between the controller
                         and its environment, and solve the parameterized
                         robust reachability problem: we show that the
                         existence of an upper bound on the perturbations
                         under which there is a strategy reaching a target
                         location is EXPTIME-complete. We also extend our
                         algorithm, with the same complexity, to turn-based
                         timed games, where the successor state is entirely
                         determined by the environment in some locations.},
}

Abstract

We study the extension of the alternating-time temporal logic (ATL) with strategy contexts: contrary to the original semantics, in this semantics the strategy quantifiers do not reset the previously selected strategies.

We show that our extension ATLsc is very expressive, but that its decision problems are quite hard: model checking is k-EXPTIME-complete when the formula has k nested strategy quantifiers; satisfiability is undecidable, but we prove that it is decidable when restricting to turn-based games. Our algorithms are obtained through a very convenient translation to QCTL (the computation-tree logic CTL extended with atomic quantification), which we show also applies to Strategy Logic, as well as when strategy quantification ranges over memoryless strategies.

@article{icomp245()-LM,
  author =              {Laroussinie, Fran{\c c}ois and Markey, Nicolas},
  title =               {Augmenting {ATL} with strategy contexts},
  publisher =           {Elsevier},
  journal =             {Information and Computation},
  volume =              {245},
  pages =               {98-123},
  year =                {2015},
  month =               dec,
  doi =                 {10.1016/j.ic.2014.12.020},
  abstract =            {We study the extension of the alternating-time
                         temporal logic (ATL) with strategy contexts:
                         contrary to the original semantics, in this
                         semantics the strategy quantifiers do not reset the
                         previously selected strategies.\par We show that our
                         extension ATLsc is very expressive, but that its
                         decision problems are quite hard: model checking is
                         \(k\)-EXPTIME-complete when the formula has \(k\)
                         nested strategy quantifiers; satisfiability is
                         undecidable, but we prove that it is decidable when
                         restricting to turn-based games. Our algorithms are
                         obtained through a very convenient translation to
                         QCTL (the~computation-tree logic CTL extended with
                         atomic quantification), which we show also applies
                         to Strategy Logic, as well as when strategy
                         quantification ranges over memoryless strategies.},
}

Abstract

Parametric timed automata (PTA) are a powerful formalism to model and reason about concurrent systems with some unknown timing delays. In this paper, we address the (untimed) language- and trace-preservation problems: given a reference parameter valuation, does there exist another parameter valuation with the same untimed language (or trace)? We show that these problems are undecidable both for general PTA, and even for the restricted class of L/U-PTA. On the other hand, we exhibit decidable subclasses: 1-clock PTA, and 1-parameter deterministic L-PTA and U-PTA.

@inproceedings{formats2015-AM,
  author =              {Andr{\'e}, {\'E}tienne and Markey, Nicolas},
  title =               {Language Preservation Problems in Parametric Timed
                         Automata},
  editor =              {Sankaranarayanan, Sriram and Vicario, Enrico},
  booktitle =           {{P}roceedings of the 13th {I}nternational
                         {C}onferences on {F}ormal {M}odelling and {A}nalysis
                         of {T}imed {S}ystems ({FORMATS}'15)},
  acronym =             {{FORMATS}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9268},
  pages =               {27-43},
  year =                {2015},
  month =               sep,
  doi =                 {10.1007/978-3-319-22975-1_3},
  abstract =            {Parametric timed automata (PTA) are a powerful
                         formalism to model and reason about concurrent
                         systems with some unknown timing delays. In this
                         paper, we address the (untimed) language- and
                         trace-preservation problems: given a reference
                         parameter valuation, does there exist another
                         parameter valuation with the same untimed language
                         (or trace)? We show that these problems are
                         undecidable both for general PTA, and even for the
                         restricted class of L/U-PTA. On the other hand, we
                         exhibit decidable subclasses: 1-clock PTA, and
                         1-parameter deterministic L-PTA and U-PTA.},
}

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

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

A weighted timed game is a timed game with extra quantitative information representing e.g. energy consumption. Optimizing the cost for reaching a target is a natural question, which has been investigated for ten years. Existence of optimal strategies is known to be undecidable in general, and only very restricted classes of games have been described for which optimal cost and almost-optimal strategies can be computed.

In this paper, we show that the value problem is undecidable in general weighted timed games. The undecidability proof relies on that for the existence of optimal strategies and on a diagonalization construction recently designed in the context of quantitative temporal logics. We then provide an algorithm to compute arbitrary approximations of the value in a game, and almost-optimal strategies. The algorithm applies in a large subclass of weighted timed games, and is the first approximation scheme which is designed in the current context.

@inproceedings{concur2015-BJM,
  author =              {Bouyer, Patricia and Jaziri, Samy and Markey,
                         Nicolas},
  title =               {On~the Value Problem in Weighted Timed Games},
  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 =               {311-324},
  year =                {2015},
  month =               sep,
  doi =                 {10.4230/LIPIcs.CONCUR.2015.311},
  abstract =            {A~weighted timed game is a timed game with extra
                         quantitative information representing e.g. energy
                         consumption. Optimizing the cost for reaching a
                         target is a natural question, which has been
                         investigated for ten years. Existence of optimal
                         strategies is known to be undecidable in general,
                         and only very restricted classes of games have been
                         described for which optimal cost and almost-optimal
                         strategies can be computed.\par In this paper, we
                         show that the value problem is undecidable in
                         general weighted timed games. The undecidability
                         proof relies on that for the existence of optimal
                         strategies and on a diagonalization construction
                         recently designed in the context of quantitative
                         temporal logics. We then provide an algorithm to
                         compute arbitrary approximations of the value in a
                         game, and almost-optimal strategies. The algorithm
                         applies in a large subclass of weighted timed games,
                         and is the first approximation scheme which is
                         designed in the current context.},
}

Abstract

The development of formal methods for control design is an important challenge with potential applications in a wide range of safety-critical cyber-physical systems. Focusing on switched dynamical systems, we propose a new abstraction, based on time-varying regions of invariance (the control funnels), that models behaviors of systems as timed automata. The main advantage of this method is that it allows automated verification of formal specifications and reactive controller synthesis without discretizing the evolution of the state of the system. Efficient constructions are possible in the case of linear dynamics. We demonstrate the potential of our approach with two examples.

@inproceedings{formats2015-BMPS,
  author =              {Bouyer, Patricia and Markey, Nicolas and Perrin,
                         Nicolas and Schlehuber{-}Caissier, Philipp},
  title =               {Timed automata abstraction of switched dynamical
                         systems using control funnels},
  editor =              {Sankaranarayanan, Sriram and Vicario, Enrico},
  booktitle =           {{P}roceedings of the 13th {I}nternational
                         {C}onferences on {F}ormal {M}odelling and {A}nalysis
                         of {T}imed {S}ystems ({FORMATS}'15)},
  acronym =             {{FORMATS}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9268},
  pages =               {60-75},
  year =                {2015},
  month =               sep,
  doi =                 {10.1007/978-3-319-22975-1_5},
  abstract =            {The~development of formal methods for control design
                         is an important challenge with potential
                         applications in a wide range of safety-critical
                         cyber-physical systems. Focusing on switched
                         dynamical systems, we~propose a new abstraction,
                         based on time-varying regions of invariance
                         (the~\emph{control funnels}), that models behaviors
                         of systems as timed automata. The main advantage of
                         this method is that it allows automated verification
                         of formal specifications and reactive controller
                         synthesis without discretizing the evolution of the
                         state of the system. Efficient constructions are
                         possible in the case of linear dynamics.
                         We~demonstrate the potential of our approach with
                         two examples.},
}

Abstract

Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the objective is to optimize the long-run average gain per action, and energy games, where the system has to avoid running out of energy.

We study average-energy games, where the goal is to optimize the long-run average of the accumulated energy. We show that this objective arises naturally in several applications, and that it yields interesting connections with previous concepts in the literature. We prove that deciding the winner in such games is in NP∩coNP and at least as hard as solving mean-payoff games, and we establish that memoryless strategies suffice to win. We also consider the case where the system has to minimize the average-energy while maintaining the accumulated energy within predefined bounds at all times: this corresponds to operating with a finite-capacity storage for energy. We give results for one-player and two-player games, and establish complexity bounds and memory requirements.

@inproceedings{gandalf2015-BMRLL,
  author =              {Bouyer, Patricia and Markey, Nicolas and Randour,
                         Mickael and Larsen, Kim Guldstrand and Laursen,
                         Simon},
  title =               {Average-energy games},
  editor =              {Esparza, Javier and Tronci, Enrico},
  booktitle =           {{P}roceedings of the 6th {I}nternational {S}ymposium
                         on {G}ames, {A}utomata, {L}ogics and {F}ormal
                         {V}erification ({GandALF}'15)},
  acronym =             {{GandALF}'15},
  series =              {Electronic Proceedings in Theoretical Computer
                         Science},
  volume =              {193},
  pages =               {1-15},
  year =                {2015},
  month =               sep,
  doi =                 {10.4204/EPTCS.193.1},
  abstract =            {Two-player quantitative zero-sum games provide a
                         natural framework to synthesize controllers with
                         performance guarantees for reactive systems within
                         an uncontrollable environment. Classical settings
                         include mean-payoff games, where the objective is to
                         optimize the long-run average gain per action, and
                         energy games, where the system has to avoid running
                         out of energy.\par We study \emph{average-energy}
                         games, where the goal is to optimize the long-run
                         average of the accumulated energy. We show that this
                         objective arises naturally in several applications,
                         and that it yields interesting connections with
                         previous concepts in the literature. We prove that
                         deciding the winner in such games is in
                         \textsf{NP}{{\(\cap\)}}\textsf{coNP} and at least as
                         hard as solving mean-payoff games, and we establish
                         that memoryless strategies suffice to win. We also
                         consider the case where the system has to minimize
                         the average-energy while maintaining the accumulated
                         energy within predefined bounds at all times: this
                         corresponds to operating with a finite-capacity
                         storage for energy. We give results for one-player
                         and two-player games, and establish complexity
                         bounds and memory requirements.},
}

Abstract

Alternating-time temporal logic with strategy contexts (ATLsc) is a powerful formalism for expressing properties of multi-agent systems: it extends CTL with strategy quantifiers, offering a convenient way of expressing both collaboration and antagonism between several agents. Incomplete observation of the state space is a desirable feature in such a framework, but it quickly leads to undecidable verification problems. In this paper, we prove that uniform incomplete observation (where all players have the same observation) preserves decidability of the model checking problem, even for very expressive logics such as ATLsc.

@inproceedings{gandalf2015-LMS,
  author =              {Laroussinie, Fran{\c c}ois and Markey, Nicolas and
                         Sangnier, Arnaud},
  title =               {{{\(\textsf{ATL}_{\textsf{sc}}\)}} with partial
                         observation},
  editor =              {Esparza, Javier and Tronci, Enrico},
  booktitle =           {{P}roceedings of the 6th {I}nternational {S}ymposium
                         on {G}ames, {A}utomata, {L}ogics and {F}ormal
                         {V}erification ({GandALF}'15)},
  acronym =             {{GandALF}'15},
  series =              {Electronic Proceedings in Theoretical Computer
                         Science},
  volume =              {193},
  pages =               {43-57},
  year =                {2015},
  month =               sep,
  doi =                 {10.4204/EPTCS.193.4},
  abstract =            {Alternating-time temporal logic with strategy
                         contexts ({{\(\textsf{ATL}_{\textsf{sc}}\)}}) is a
                         powerful formalism for expressing properties of
                         multi-agent systems: it~extends \textsf{CTL} with
                         \emph{strategy quantifiers}, offering a convenient
                         way of expressing both collaboration and antagonism
                         between several agents. Incomplete observation of
                         the state space is a desirable feature in such a
                         framework, but it quickly leads to undecidable
                         verification problems. In this paper, we prove that
                         \emph{uniform} incomplete observation (where all
                         players have the same observation) preserves
                         decidability of the model checking problem, even for
                         very expressive logics such as
                         {{\(\textsf{ATL}_{\textsf{sc}}\)}}.},
}

Abstract

In this report, the program, research issues, and results of Dagstuhl Seminar 15061 "Non-Zero-Sum-Games and Control" are described. The area of non-zero-sum games is addressed in a wide range of topics: multi-player games, partial-observation games, quantitative game models, and—as a special focus—connections with control engineering (supervisory control).

@proceedings{dagrep5(2)-CLMT,
  title =               {Non-Zero-Sum-Games and Control ({D}agstuhl
                         Seminar~15061)},
  editor =              {Chatterjee, Krishnendu and Lafortune, St{\'e}phane
                         and Markey, Nicolas and Thomas, Wolfgang},
  booktitle =           {Non-Zero-Sum-Games and Control ({D}agstuhl
                         Seminar~15061)},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  journal =             {Dagstuhl Reports},
  volume =              {5},
  number =              {2},
  pages =               {1-25},
  year =                {2015},
  month =               jun,
  doi =                 {10.4230/DagRep.5.2.1},
  url =                 {http://drops.dagstuhl.de/opus/volltexte/2015/5042},
  abstract =            {In this report, the program, research issues, and
                         results of Dagstuhl Seminar~15061
                         {"}Non-Zero-Sum-Games and Control{"} are described.
                         The area of non-zero-sum games is addressed in a
                         wide range of topics: multi-player games,
                         partial-observation games, quantitative game models,
                         and---as~a special focus---connections with control
                         engineering (supervisory control).},
}

@article{jacm62(1)-AAGT,
  author =              {Agrawal, Manindra and Akshay, S. and Genest, Blaise
                         and Thiagarajan, P. S.},
  title =               {Approximate Verification of the Symbolic Dynamics of
                         {M}arkov Chains},
  publisher =           {ACM Press},
  journal =             {Journal of the~ACM},
  volume =              {62},
  number =              {1},
  pages =               {183-235},
  year =                {2015},
  month =               feb,
  doi =                 {10.1145/2629417},
}

@inproceedings{concur2015-ABG,
  author =              {Aiswarya, C. and Bollig, Benedikt and Gastin, Paul},
  title =               {An automata-theoretic approach to the verification
                         of distributed algorithms},
  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 =               {340-353},
  year =                {2015},
  month =               sep,
  doi =                 {10.4230/LIPIcs.CONCUR.2015.340},
}

@inproceedings{fsttcs2015-AKK,
  author =              {Almagor, Shaull and Kuperberg, Denis and Kupferman,
                         Orna},
  title =               {The~Sensing Cost of Monitoring and Synthesis},
  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 =               {380-393},
  year =                {2015},
  month =               dec,
  doi =                 {10.4230/LIPIcs.FSTTCS.2015.380},
}

@inproceedings{lpar2015-ARZ,
  author =              {Aminof, Benjamin and Rubin, Sasha and Zuleger,
                         Florian},
  title =               {On the Expressive Power of Communication Primitives
                         in Parameterised Systems},
  editor =              {Davis, Martin and Fehnker, Ansgar and McIver,
                         Annabelle K. and Voronkov, Andrei},
  booktitle =           {{P}roceedings of the 20th {I}nternational
                         {C}onference {L}ogic {P}rogramming and {A}utomated
                         {R}easoning ({LPAR}'15)},
  acronym =             {{LPAR}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9450},
  pages =               {313-328},
  year =                {2015},
  month =               nov,
  doi =                 {10.1007/978-3-662-48899-7_22},
}

@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{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},
}

@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{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},
}

@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},
}

@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},
}

@inproceedings{atva2015-BMV,
  author =              {Berwanger, Dietmar and Mathew, Anup Basil and
                         Van{~}den{ }Bogaard, Marie},
  title =               {Hierarchical Information Patterns and Distributed
                         Strategy Synthesis},
  editor =              {Finkbeiner, Bernd and Pu, Geguang and Zhang, Lijun},
  booktitle =           {{P}roceedings of the 13th {I}nternational
                         {S}ymposium on {A}utomated {T}echnology for
                         {V}erification and {A}nalysis ({ATVA}'15)},
  acronym =             {{ATVA}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9364},
  pages =               {378-393},
  year =                {2015},
  month =               oct,
}

@article{fmsd46(1)-BSJK,
  author =              {Bertrand, Nathalie and Stainer, Am{\'e}lie and
                         J{\'e}ron, Thierry and Krichen, Moez},
  title =               {A~game approach to determinize timed automata},
  publisher =           {Springer-Verlag},
  journal =             {Formal Methods in System Design},
  volume =              {46},
  number =              {1},
  pages =               {42-80},
  year =                {2015},
  month =               feb,
  doi =                 {10.1007/s10703-014-0220-1},
}

@article{icomp242()-CDRR,
  author =              {Chatterjee, Krishnendu and Doyen, Laurent and
                         Randour, Mickael and Raskin, Jean-Fran{\c c}ois},
  title =               {Looking at Mean-Payoff and Total-Payoff through
                         Windows},
  publisher =           {Elsevier},
  journal =             {Information and Computation},
  volume =              {242},
  pages =               {25-52},
  year =                {2015},
  month =               jun,
  doi =                 {10.1016/j.ic.2015.03.010},
}

@inproceedings{aaai2015-CLM,
  author =              {{\v{C}}erm{\'a}k, Petr and Lomuscio, Alessio and
                         Murano, Aniello},
  title =               {Verifying and Synthesising Multi-Agent Systems
                         against One-Goal Strategy Logic Specifications},
  editor =              {Bonet, Blai and Koenig, Sven},
  booktitle =           {{P}roceedings of the 29th {AAAI} {C}onference on
                         {A}rtificial {I}ntelligence ({AAAI}'15)},
  acronym =             {{AAAI}'15},
  publisher =           {AAAI Press},
  pages =               {2038-2044},
  year =                {2015},
  month =               jan,
}

@inproceedings{cav2015-DEGM,
  author =              {Durand{-}Gasselin, Antoine and Esparza, Javier and
                         Ganty, Pierre and Majumdar, Rupak},
  title =               {Model Checking Parameterized Asynchronous
                         Shared-Memory Systems},
  editor =              {Kroening, Daniel and Pasareanu, Corina S.},
  booktitle =           {{P}roceedings of the 27th {I}nternational
                         {C}onference on {C}omputer {A}ided {V}erification
                         ({CAV}'15)},
  acronym =             {{CAV}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9206},
  pages =               {67-84},
  year =                {2015},
  month =               jul,
  doi =                 {10.1007/978-3-319-21690-4_5},
}

@inproceedings{tacas2015-DLLMW,
  author =              {David, Alexandre and Jensen, Peter Gj{\o}l and
                         Larsen, Kim Guldstrand and Miku{\v{c}}ionis, Marius
                         and Taankvist, Jakob Haar},
  title =               {Uppaal Stratego},
  editor =              {Baier, {\relax Ch}ristel and Tinelli, Cesare},
  booktitle =           {{P}roceedings of the 21st {I}nternational
                         {C}onference on {T}ools and {A}lgorithms for
                         {C}onstruction and {A}nalysis of {S}ystems
                         ({TACAS}'15)},
  acronym =             {{TACAS}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9035},
  pages =               {206-211},
  year =                {2015},
  month =               apr,
  doi =                 {10.1007/978-3-662-46681-0_16},
}

@inproceedings{icalp2015-DKMSZ,
  author =              {Datta, Samir and Kulkarni, Raghav and Mukherjee,
                         Anish and Schwentick, Thomas and Zeume, Thomas},
  title =               {Reachability is in {D}yn{F}O},
  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 =               {159-170},
  year =                {2015},
  month =               jul,
  doi =                 {10.1007/978-3-662-47666-6_13},
}

@inproceedings{cav2015-DSQBE,
  author =              {Desai, Ankush and Seshia,Sanjit A. and Qadeer, Shaz
                         and Broman, David and Eidson, John C.},
  title =               {Approximate synchrony: An abstraction for
                         distributed almost-synchronous systems},
  editor =              {Kroening, Daniel and Pasareanu, Corina S.},
  booktitle =           {{P}roceedings of the 27th {I}nternational
                         {C}onference on {C}omputer {A}ided {V}erification
                         ({CAV}'15)},
  acronym =             {{CAV}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9206},
  pages =               {429-448},
  year =                {2015},
  month =               jul,
  doi =                 {10.1007/978-3-319-21668-3_25},
}

@inproceedings{concur2015-EGLM,
  author =              {Esparza, Javier and Ganty, Pierre and Leroux,
                         J{\'e}r{\^o}me and Majumdar, Rupak},
  title =               {Verification of Population Protocols},
  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 =               {470-482},
  year =                {2015},
  month =               sep,
  doi =                 {10.4230/LIPIcs.CONCUR.2015.470},
}

@phdthesis{phd-fournier,
  author =              {Fournier, Paulin},
  title =               {Parameterized verification of networks of many
                         identical processes},
  year =                {2015},
  month =               dec,
  school =              {Universit{\'e} Rennes~1, France},
  type =                {Th\`ese de doctorat},
}

@techreport{arxiv1503.07193-FT,
  author =              {Fu, Jie and Topcu, Ufuk},
  title =               {Computational methods for stochastic control with
                         metric interval temporal logic specifications},
  number =              {1503.07193},
  year =                {2015},
  month =               mar,
  institution =         {arXiv},
  type =                {Research Report},
}

@inproceedings{fossacs2015-Gan,
  author =              {Ganardi, Moses},
  title =               {Parity Games of Bounded Tree- and Clique-Width},
  editor =              {Pitts, Andrew},
  booktitle =           {{P}roceedings of the 18th {I}nternational
                         {C}onference on {F}oundations of {S}oftware
                         {S}cience and {C}omputation {S}tructure
                         ({FoSSaCS}'15)},
  acronym =             {{FoSSaCS}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9034},
  pages =               {390-404},
  year =                {2015},
  month =               apr,
  doi =                 {10.1007/978-3-662-46678-0_25},
}

@inproceedings{formats2015-HT,
  author =              {Herbreteau, Fr{\'e}d{\'e}ric and Tran, Thanh-Tung},
  title =               {Improving Search Order for Reachability Testing in
                         Timed Automata},
  editor =              {Sankaranarayanan, Sriram and Vicario, Enrico},
  booktitle =           {{P}roceedings of the 13th {I}nternational
                         {C}onferences on {F}ormal {M}odelling and {A}nalysis
                         of {T}imed {S}ystems ({FORMATS}'15)},
  acronym =             {{FORMATS}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9268},
  pages =               {124-139},
  year =                {2015},
  month =               sep,
  doi =                 {10.1007/978-3-319-22975-1_9},
}

@inproceedings{rp2015-Hun,
  author =              {Hunter, Paul},
  title =               {Reachability in Succinct One-Counter Games},
  editor =              {Boja{\'n}czyk, Miko{\l}aj and Lasota, S{\l}awomir
                         and Potapov, Igor},
  booktitle =           {{P}roceedings of the 9th {W}orkshop on
                         {R}eachability {P}roblems in {C}omputational
                         {M}odels ({RP}'15)},
  acronym =             {{RP}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9328},
  pages =               {37-49},
  year =                {2015},
  month =               sep,
  doi =                 {10.1007/978-3-319-24537-9_5},
}

@article{tse41(5)-JLR,
  author =              {Jovanovi{\'c}, Aleksandra and Lime, Didier and Roux,
                         Olivier H.},
  title =               {Integer Parameter Synthesis for Timed Automata},
  publisher =           {IEEE Comp. Soc. Press},
  journal =             {IEEE Transactions on Software Engineering},
  volume =              {41},
  number =              {5},
  pages =               {445-461},
  year =                {2015},
  month =               may,
  doi =                 {10.1109/TSE.2014.2357445},
}

@inproceedings{icalp2015-JLS,
  author =              {Jurdzi{\'n}ski, Marcin and Lazi{\'c}, Ranko and
                         Schmitz, Sylvain},
  title =               {Fixed-Dimensional Energy Games are in
                         Pseudo-Polynomial Time},
  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 =               {260-272},
  year =                {2015},
  month =               jul,
  doi =                 {10.1007/978-3-662-47666-6_21},
}

@inproceedings{icalp2015-KS,
  author =              {Kuperberg, Denis and Skrzypczak, Michal},
  title =               {On determinisation of good-for-games 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 =               {299-310},
  year =                {2015},
  month =               jul,
  doi =                 {10.1007/978-3-662-47666-6_24},
}

@inproceedings{cav2015-KVW,
  author =              {Konnov, Igor V. and Veith, Helmut and Widder, Josef},
  title =               {{SMT} and {POR} bea Counter Abstraction:
                         Parameterized Model Checking of Threshold-Based
                         Distributed Algorithms},
  editor =              {Kroening, Daniel and Pasareanu, Corina S.},
  booktitle =           {{P}roceedings of the 27th {I}nternational
                         {C}onference on {C}omputer {A}ided {V}erification
                         ({CAV}'15)},
  acronym =             {{CAV}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9206},
  pages =               {85-102},
  year =                {2015},
  month =               jul,
  doi =                 {10.1007/978-3-319-21690-4_6},
}

@techreport{arxiv-1510.05774,
  author =              {Larsen, Kim Guldstrand and Laursen, Simon and
                         Zimmermann, Martin},
  title =               {Limit Your Consumption! Finding Bounds in
                         Average-energy Games},
  number =              {1510.05774},
  year =                {2015},
  month =               oct,
  institution =         {arXiv},
  type =                {Research Report},
}

@techreport{arxiv-1512.05511,
  author =              {Mu{\~n}oz, Pablo and Vortmeier, Nils and Zeume,
                         Thomas},
  title =               {Dynamic Graph Queries},
  number =              {1512.05511},
  year =                {2015},
  month =               dec,
  institution =         {arXiv},
  type =                {Research Report},
}

@inproceedings{tacas2015-San,
  author =              {Sankur, Ocan},
  title =               {Symbolic Quantitative Robustness Analysis of Timed
                         Automata},
  editor =              {Baier, {\relax Ch}ristel and Tinelli, Cesare},
  booktitle =           {{P}roceedings of the 21st {I}nternational
                         {C}onference on {T}ools and {A}lgorithms for
                         {C}onstruction and {A}nalysis of {S}ystems
                         ({TACAS}'15)},
  acronym =             {{TACAS}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9035},
  pages =               {484-498},
  year =                {2015},
  month =               apr,
  doi =                 {10.1007/978-3-662-46681-0_48},
}

@inproceedings{tacas2015-Thi,
  author =              {Thierry{-}Mieg, Yann},
  title =               {Symbolic Model-Checking Using {ITS}-Tools},
  editor =              {Baier, {\relax Ch}ristel and Tinelli, Cesare},
  booktitle =           {{P}roceedings of the 21st {I}nternational
                         {C}onference on {T}ools and {A}lgorithms for
                         {C}onstruction and {A}nalysis of {S}ystems
                         ({TACAS}'15)},
  acronym =             {{TACAS}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9035},
  pages =               {231-237},
  year =                {2015},
  month =               apr,
  doi =                 {10.1007/978-3-662-46681-0_20},
}

@article{icomp241()-VCDHRR,
  author =              {Velner, Yaron and Chatterjee, Krishnendu and Doyen,
                         Laurent and Henzinger, Thomas A. and Rabinovich,
                         Alexander and Raskin, Jean-Fran{\c c}ois},
  title =               {The complexity of multi-mean-payoff and multi-energy
                         games},
  publisher =           {Elsevier},
  journal =             {Information and Computation},
  volume =              {241},
  pages =               {177-196},
  year =                {2015},
  month =               apr,
  doi =                 {10.1016/j.ic.2015.03.001},
}

@inproceedings{atva2015-Ves,
  author =              {Vester, Steen},
  title =               {On the Complexity of Model-checking Branching and
                         Alternating-time Temporal Logics in One-counter
                         systems},
  editor =              {Finkbeiner, Bernd and Pu, Geguang and Zhang, Lijun},
  booktitle =           {{P}roceedings of the 13th {I}nternational
                         {S}ymposium on {A}utomated {T}echnology for
                         {V}erification and {A}nalysis ({ATVA}'15)},
  acronym =             {{ATVA}'15},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9364},
  pages =               {361-377},
  year =                {2015},
  month =               oct,
  doi =                 {10.1007/978-3-319-24953-7_27},
}

@article{toplas37(3)-WSH,
  author =              {Wang, Farn and Schewe, Sven and Huang, Chung-Hao},
  title =               {An~extension of~{ATL} with Strategy Interaction},
  publisher =           {ACM Press},
  journal =             {ACM Transactions on Programming Languages and
                         Systems},
  volume =              {37},
  number =              {3},
  year =                {2015},
  month =               jun,
  doi =                 {10.1145/2734117},
}

@phdthesis{phd-zeume,
  author =              {Zeume, Thomas},
  title =               {Small Dynamic Complexity Classes},
  year =                {2015},
  month =               may,
  school =              {Dortmund University, Germany},
  type =                {{PhD} thesis},
}