Nicolas Markey

Résumé

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 with the same set of traces? We show that these problems are undecidable both for general PTA and for the restricted class of L/U-PTA, even for integer-valued parameters, or over bounded time. On the other hand, we exhibit decidable subclasses: 1-clock PTA, and 1-parameter deterministic L-PTA and U-PTA. We also consider robust versions of these problems, where we additionally require that the language be preserved for all valuations between the reference valuation and the new valuation.

@article{lmcs16(1)-ALM,
  author =              {Andr{\'e}, {\'E}tienne and Lime, Didier and Markey,
                         Nicolas},
  title =               {Language-preservation problems in parametric timed
                         automata},
  journal =             {Logical Methods in Computer Science},
  volume =              {16},
  number =              {1},
  year =                {2020},
  month =               jan,
  doi =                 {10.23638/LMCS-16(1:5)2020},
  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 with the same set of traces? We~show that these
                         problems are undecidable both for general PTA and
                         for the restricted class of L{\slash}U-PTA, even for
                         integer-valued parameters, or over bounded time.
                         On~the other~hand, we~exhibit decidable subclasses:
                         1-clock PTA, and 1-parameter deterministic L-PTA and
                         U-PTA. We~also consider robust versions of these
                         problems, where we additionally require that the
                         language be preserved for all valuations between the
                         reference valuation and the new valuation.},
}

Résumé

Strategy Logic (SL) is a very expressive temporal logic for specifying and verifying properties of multi-agent systems: in SL, one can quantify over strategies, assign them to agents, and express LTL properties of the resulting plays. Such a powerful framework has two drawbacks: first, model checking SL has non-elementary complexity; second, the exact semantics of SL is rather intricate, and may not correspond to what is expected. In this paper, we focus on strategy dependences in SL, by tracking how existentially-quantified strategies in a formula may (or may not) depend on other strategies selected in the formula, revisiting the approach of [Mogavero et al., Reasoning about strategies: On the model-checking problem, 2014]. We explain why elementary dependences, as defined by Mogavero et al., do not exactly capture the intended concept of behavioral strategies. We address this discrepancy by introducing timeline dependences, and exhibit a large fragment of SL for which model checking can be performed in 2EXPTIME under this new semantics.

@article{tocsys64(3)-GBM,
  author =              {Gardy, Patrick and Bouyer, Patricia and Markey,
                         Nicolas},
  title =               {Dependences in Strategy Logic},
  publisher =           {Springer-Verlag},
  journal =             {Theory of Computing Systems},
  volume =              {64},
  number =              {3},
  pages =               {467-507},
  year =                {2020},
  month =               apr,
  doi =                 {10.1007/s00224-019-09926-y},
  abstract =            {Strategy Logic~(\textsf{SL}) is a very expressive
                         temporal logic for specifying and verifying
                         properties of multi-agent systems: in~\textsf{SL},
                         one can quantify over strategies, assign them to
                         agents, and express \textsf{LTL} properties of the
                         resulting plays. Such a powerful framework has two
                         drawbacks: first, model checking \textsf{SL} has
                         non-elementary complexity; second, the exact
                         semantics of \textsf{SL} is rather intricate, and
                         may not correspond to what is expected. In~this
                         paper, we~focus on \emph{strategy dependences}
                         in~\textsf{SL}, by tracking how
                         existentially-quantified strategies in a formula may
                         (or~may~not) depend on other strategies selected in
                         the formula, revisiting the approach of~[Mogavero
                         \emph{et~al.}, Reasoning about strategies: On~the
                         model-checking problem,~2014]. We~explain why
                         \emph{elementary} dependences, as defined by
                         Mogavero~\emph{et~al.}, do not exactly capture the
                         intended concept of behavioral strategies.
                         We~address this discrepancy by introducing
                         \emph{timeline} dependences, and exhibit a large
                         fragment of \textsf{SL} for which model checking can
                         be performed in \textsf{2EXPTIME} under this new
                         semantics.},
}

Résumé

Congestion games are a classical type of games studied in game theory, in which n players choose a resource, and their individual cost increases with the number of other players choosing the same resource. In network congestion games (NCGs), the resources correspond to simple paths in a graph, e.g. representing routing options from a source to a target. In this paper, we introduce a variant of NCGs, referred to as dynamic NCGs: in this setting, players take transitions synchronously, they select their next transitions dynamically, and they are charged a cost that depends on the number of players simultaneously using the same transition.

We study, from a complexity perspective, standard concepts of game theory in dynamic NCGs: social optima, Nash equilibria, and subgame perfect equilibria. Our contributions are the following: the existence of a strategy profile with social cost bounded by a constant is in PSPACE and NP-hard. (Pure) Nash equilibria always exist in dynamic NCGs; the existence of a Nash equilibrium with bounded cost can be decided in EXPSPACE, and computing a witnessing strategy profile can be done in doubly-exponential time. The existence of a subgame perfect equilibrium with bounded cost can be decided in 2EXPSPACE, and a witnessing strategy profile can be computed in triply-exponential time.

@inproceedings{fsttcs2020-BMSS,
  author =              {Bertrand, Nathalie and Markey, Nicolas and
                         Sadhukhan, Suman and Sankur, Ocan},
  title =               {Dynamic network congestion games},
  editor =              {Saxena, Nitin and Simon, Sunil},
  booktitle =           {{P}roceedings of the 40th {C}onference on
                         {F}oundations of {S}oftware {T}echnology and
                         {T}heoretical {C}omputer {S}cience ({FSTTCS}'20)},
  acronym =             {{FSTTCS}'20},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {182},
  pages =               {40:1-40:16},
  year =                {2020},
  month =               dec,
  doi =                 {10.4230/LIPIcs.FSTTCS.2020.40},
  abstract =            {Congestion games are a classical type of games
                         studied in game theory, in which n players choose a
                         resource, and their individual cost increases with
                         the number of other players choosing the same
                         resource. In network congestion games~(NCGs), the
                         resources correspond to simple paths in a graph,
                         e.g.~representing routing options from a source to a
                         target. In this paper, we introduce a variant
                         of~NCGs, referred to as dynamic~NCGs: in~this
                         setting, players take transitions synchronously,
                         they select their next transitions dynamically, and
                         they are charged a cost that depends on the number
                         of players simultaneously using the same transition.
                         \par We~study, from a complexity perspective,
                         standard concepts of game theory in dynamic NCGs:
                         social optima, Nash equilibria, and subgame perfect
                         equilibria. Our contributions are the following: the
                         existence of a strategy profile with social cost
                         bounded by a constant is in PSPACE and NP-hard.
                         (Pure)~Nash equilibria always exist in dynamic~NCGs;
                         the existence of a Nash equilibrium with bounded
                         cost can be decided in EXPSPACE, and computing a
                         witnessing strategy profile can be done in
                         doubly-exponential time. The~existence of a subgame
                         perfect equilibrium with bounded cost can be decided
                         in 2EXPSPACE, and a witnessing strategy profile can
                         be computed in triply-exponential~time.},
}

Résumé

Timed automata are a convenient mathematical model for modelling and reasoning about real-time systems. While they provide a powerful way of representing timing aspects of such systems, timed automata assume arbitrary precision and zero-delay actions; in particular, a state might be declared reachable in a timed automaton, but impossible to reach in the physical system it models.

In this paper, we consider permissive strategies as a way to overcome this problem: such strategies propose intervals of delays instead of single delays, and aim at reaching a target state whichever delay actually takes place. We develop an algorithm for computing the optimal permissiveness (and an associated maximally-permissive strategy) in acyclic timed automata and games.

@inproceedings{formats2020-CJMM,
  author =              {Clement, Emily and J{\'e}ron, Thierry and Markey,
                         Nicolas and Mentr{\'e}, David},
  title =               {Computing maximally-permissive strategies in acyclic
                         timed automata},
  editor =              {Bertrand, Nathalie and Jansen, Nils},
  booktitle =           {{P}roceedings of the 18th {I}nternational
                         {C}onferences on {F}ormal {M}odelling and {A}nalysis
                         of {T}imed {S}ystems ({FORMATS}'20)},
  acronym =             {{FORMATS}'20},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {12288},
  pages =               {111-126},
  year =                {2020},
  month =               sep,
  doi =                 {10.1007/978-3-030-57628-8_7},
  abstract =            {Timed automata are a convenient mathematical model
                         for modelling and reasoning about real-time systems.
                         While they provide a powerful way of representing
                         timing aspects of such systems, timed automata
                         assume arbitrary precision and zero-delay actions;
                         in~particular, a~state might be declared reachable
                         in a timed automaton, but impossible to reach in the
                         physical system it models. \par In this paper, we
                         consider permissive strategies as a way to overcome
                         this problem: such strategies propose intervals of
                         delays instead of single delays, and aim at reaching
                         a target state whichever delay actually takes place.
                         We develop an algorithm for computing the optimal
                         permissiveness (and~an associated
                         maximally-permissive strategy) in acyclic timed
                         automata and games.},
}

Résumé

Active learning of timed languages is concerned with the inference of timed automata by observing some of the timed words in their languages. The learner can query for the membership of words in the language, or propose a candidate model and ask if it is equivalent to the target. The major difficulty of this framework is the inference of clock resets, which are central to the dynamics of timed automata but not directly observable.

Interesting first steps have already been made by restricting to the subclass of event-recording automata, where clock resets are tied to observations. In order to advance towards learning of general timed automata, we generalize this method to a new class, called reset-free event-recording automata, where some transitions may reset no clocks.

Central to our contribution is the notion of invalidity, and the algorithm and data structures to deal with it, allowing on-the-fly detection and pruning of reset hypotheses that contradict observations. This notion is a key to any efficient active-learning procedure for generic timed automata.

@inproceedings{formats2020-HJM,
  author =              {Henry, L{\'e}o and J{\'e}ron, Thierry and Markey,
                         Nicolas},
  title =               {Active learning of timed automata with unobservable
                         resets},
  editor =              {Bertrand, Nathalie and Jansen, Nils},
  booktitle =           {{P}roceedings of the 18th {I}nternational
                         {C}onferences on {F}ormal {M}odelling and {A}nalysis
                         of {T}imed {S}ystems ({FORMATS}'20)},
  acronym =             {{FORMATS}'20},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {12288},
  pages =               {144-160},
  year =                {2020},
  month =               sep,
  doi =                 {10.1007/978-3-030-57628-8_9},
  abstract =            {Active learning of timed languages is concerned with
                         the inference of timed automata by observing some of
                         the timed words in their languages. The learner can
                         query for the membership of words in the language,
                         or propose a candidate model and ask if it is
                         equivalent to the target. The major difficulty of
                         this framework is the inference of clock resets,
                         which are central to the dynamics of timed automata
                         but not directly observable. \par Interesting first
                         steps have already been made by restricting to the
                         subclass of event-recording automata, where clock
                         resets are tied to observations. In order to advance
                         towards learning of general timed automata, we
                         generalize this method to a new class, called
                         reset-free event-recording automata, where some
                         transitions may reset no clocks. \par Central to our
                         contribution is the notion of invalidity, and the
                         algorithm and data structures to deal with it,
                         allowing on-the-fly detection and pruning of reset
                         hypotheses that contradict observations. This notion
                         is a key to any efficient active-learning procedure
                         for generic timed automata.},
}

Résumé

Requirements engineering is a key phase in the development process. Ensuring that requirements are consistent is essential so that they do not conflict and admit implementations. We consider the formal verification of rt-consistency, which imposes that the inevitability of definitive errors of a requirement should be anticipated, and that of partial consistency, which was recently introduced as a more effective check. We generalize and formalize both notions for discrete-time timed automata, develop three incremental algorithms, and present experimental results.

@inproceedings{formats2020-JMMNS,
  author =              {J{\'e}ron, Thierry and Markey, Nicolas and
                         Mentr{\'e}, David and Noguchi, Reiya and Sankur,
                         Ocan},
  title =               {Incremental methods for checking real-time
                         consistency},
  editor =              {Bertrand, Nathalie and Jansen, Nils},
  booktitle =           {{P}roceedings of the 18th {I}nternational
                         {C}onferences on {F}ormal {M}odelling and {A}nalysis
                         of {T}imed {S}ystems ({FORMATS}'20)},
  acronym =             {{FORMATS}'20},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {12288},
  pages =               {249-264},
  year =                {2020},
  month =               sep,
  doi =                 {10.1007/978-3-030-57628-8_15},
  abstract =            {Requirements engineering is a key phase in the
                         development process. Ensuring that requirements are
                         consistent is essential so that they do not conflict
                         and admit implementations. We~consider the formal
                         verification of rt-consistency, which imposes that
                         the inevitability of definitive errors of a
                         requirement should be anticipated, and that of
                         partial consistency, which was recently introduced
                         as a more effective check. We~generalize and
                         formalize both notions for discrete-time timed
                         automata, develop three incremental algorithms, and
                         present experimental results.},
}

@inproceedings{tacas2020-ACZZZ,
  author =              {An, Jie and Chen, Mingshuai and Zhan, Bohua and
                         Zhan, Naijun and Zhang, Miaomiao},
  title =               {Learning One-Clock Timed Automata},
  editor =              {Biere, Armin and Parker, David},
  booktitle =           {{P}roceedings of the 26th {I}nternational
                         {C}onference on {T}ools and {A}lgorithms for
                         {C}onstruction and {A}nalysis of {S}ystems
                         ({TACAS}'20)~-- {P}art~{I}},
  acronym =             {{TACAS}'20 (Part~{I})},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {12078},
  pages =               {444-462},
  year =                {2020},
  month =               apr,
  doi =                 {10.1007/978-3-030-45190-5_25},
}

@article{tcs807()-AHK,
  author =              {Avni, Guy and Henzinger, Thomas A. and Kupferman,
                         Orna},
  title =               {Dynamic Resource Allocation Games},
  publisher =           {Elsevier},
  journal =             {Theoretical Computer Science},
  volume =              {807},
  pages =               {42-55},
  year =                {2020},
  month =               feb,
  doi =                 {10.1016/j.tcs.2019.06.031},
}

@techreport{arxiv-AMPR,
  author =              {Amram, Gal and Maoz, Shahar and Pistiner, Or and
                         Ringert, Jan Oliver},
  title =               {Energy {{\(\mu\)}}-Calculus: Symbolic Fixed-Point
                         Algorithms for {{\(\omega\)}}-Regular Energy Games},
  number =              {2005.00641},
  year =                {2020},
  month =               may,
  institution =         {arXiv},
}

@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},
}

@inproceedings{fsttcs2020-BKLS,
  author =              {Boker, Udi and Kuperberg, Denis and Lehtinen,
                         Karoliina and Skrzypczak, Michal},
  title =               {On succinctness and recognisability of alternating
                         good-for-games automata},
  editor =              {Saxena, Nitin and Simon, Sunil},
  booktitle =           {{P}roceedings of the 40th {C}onference on
                         {F}oundations of {S}oftware {T}echnology and
                         {T}heoretical {C}omputer {S}cience ({FSTTCS}'20)},
  acronym =             {{FSTTCS}'20},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {182},
  pages =               {41:1-41:13},
  year =                {2020},
  month =               dec,
  doi =                 {10.4230/LIPIcs.FSTTCS.2020.41},
}

@article{or68(2)-CCMS,
  author =              {Colini{-}Baldeschi, Riccardo and Cominetti, Roberto
                         and Mertikopoulos, Panayotis and Scarsini, Marco},
  title =               {When is selfish routing bad? {T}he~price of anarchy
                         in light and heavy traffic},
  publisher =           {Informs},
  journal =             {Operations Research},
  volume =              {68},
  number =              {2},
  pages =               {411-434},
  year =                {2020},
  month =               apr,
  doi =                 {10.1287/opre.2019.1894},
}

@book{Had20-IEDES,
  author =              {Hadjicostis, Christoforos N.},
  title =               {Estimation and Inference in Discrete Event
                         Systems~-- A~model-based approach with finite
                         automata},
  publisher =           {Springer-Verlag},
  series =              {Communications and Control Engineering},
  year =                {2020},
}

@inproceedings{lics2020-LZ,
  author =              {Lehtinen, Karoliina and Zimmermann, Martin},
  title =               {Good-for-games {\(\omega\)}-pushdown automata},
  editor =              {Hermanns, Holger and Zhang, Lijun and Kobayashi,
                         Naoki and Miller, Dale},
  booktitle =           {{P}roceedings of the 35th {A}nnual {S}ymposium on
                         {L}ogic in {C}omputer {S}cience ({LICS}'20)},
  acronym =             {{LICS}'20},
  publisher =           {IEEE Comp. Soc. Press},
  pages =               {689-702},
  year =                {2020},
  month =               jul,
  doi =                 {10.1145/3373718.3394737},
}

@techreport{arxiv2001.07141-MMPSS,
  author =              {Maubert, Bastien and Murano, Aniello and Pinchinat,
                         Sophie and Schwarzentruber, Fran{\c c}ois and
                         Stranieri, Silvia},
  title =               {Dynamic Epistemic Logic Games with Epistemic
                         Temporal Goals},
  number =              {2001-07141},
  year =                {2020},
  month =               jan,
  institution =         {arXiv},
}

@phdthesis{phd-roussanaly,
  author =              {Roussanaly, Victor},
  title =               {Efficient verification of real-time systems},
  year =                {2020},
  month =               nov,
  school =              {Universit{\'e} Rennes~1, France},
  type =                {Th\`ese de doctorat},
}

@inproceedings{fsttcs2020-Wol,
  author =              {Wolf, Petra},
  title =               {Synchronization under Dynamic Constraints},
  editor =              {Saxena, Nitin and Simon, Sunil},
  booktitle =           {{P}roceedings of the 40th {C}onference on
                         {F}oundations of {S}oftware {T}echnology and
                         {T}heoretical {C}omputer {S}cience ({FSTTCS}'20)},
  acronym =             {{FSTTCS}'20},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {182},
  pages =               {58:1-58:14},
  year =                {2020},
  month =               dec,
  doi =                 {10.4230/LIPIcs.FSTTCS.2020.58},
}