18 Search Results for "Bruyère, Véronique"

Document
DOI: 10.4230/LIPIcs.CSL.2026.8
Register-Bounded Synthesis from Constraint LTL

Authors: Nino Dauvier, Emmanuel Filiot, and Pierre-Alain Reynier

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
We consider synthesis problems from logical specifications over infinite data domains, expressed in the logic constraint LTL (CLTL), which extends LTL with predicates over an infinite set of data values. We consider register-bounded synthesis, where the goal is to automatically generate, if it exists, a transducer with r registers that realizes a given CLTL formula, where r is also given as input. We prove that CLTL register-bounded synthesis is 2ExpTime-c for various data domains such as any infinite set with equality, (ℚ, <), and (ℕ, <). For the latter domain, this contrasts with known undecidability results of (unbounded) register CLTL synthesis, by Bhaskar and Praveen. Lastly, we consider synthesis in a partial observation setting by extending CLTL with invisible variables.
Cite as

Nino Dauvier, Emmanuel Filiot, and Pierre-Alain Reynier. Register-Bounded Synthesis from Constraint LTL. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dauvier_et_al:LIPIcs.CSL.2026.8,
  author =	{Dauvier, Nino and Filiot, Emmanuel and Reynier, Pierre-Alain},
  title =	{{Register-Bounded Synthesis from Constraint LTL}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.8},
  URN =		{urn:nbn:de:0030-drops-254322},
  doi =		{10.4230/LIPIcs.CSL.2026.8},
  annote =	{Keywords: Synthesis, Data words, Constraint linear time logic, Register transducer}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.33
A Zone-Based Algorithm for Timed Parity Games

Authors: Gilles Geeraerts, Frédéric Herbreteau, Jean-François Raskin, and Alexis Reynouard

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
This paper revisits timed games by building upon the semantics introduced in "The Element of Surprise in Timed Games" [Luca de Alfaro et al., 2003]. We introduce some modifications to this semantics for two primary reasons: firstly, we recognize instances where the original semantics appears counterintuitive in the context of controller synthesis; secondly, we present methods to develop efficient zone-based algorithms. Our algorithm successfully addresses timed parity games, and we have implemented it using UPPAAL’s zone library. This prototype effectively demonstrates the feasibility of a zone-based algorithm for parity objectives and a rich semantics for timed interactions between the players.
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Gilles Geeraerts, Frédéric Herbreteau, Jean-François Raskin, and Alexis Reynouard. A Zone-Based Algorithm for Timed Parity Games. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 33:1-33:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{geeraerts_et_al:LIPIcs.FSTTCS.2025.33,
  author =	{Geeraerts, Gilles and Herbreteau, Fr\'{e}d\'{e}ric and Raskin, Jean-Fran\c{c}ois and Reynouard, Alexis},
  title =	{{A Zone-Based Algorithm for Timed Parity Games}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{33:1--33:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.33},
  URN =		{urn:nbn:de:0030-drops-251140},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.33},
  annote =	{Keywords: Timed Parity Games, Realtime Controller Synthesis}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.35
Scalable Learning of One-Counter Automata via State-Merging Algorithms

Authors: Shibashis Guha, Anirban Majumdar, Prince Mathew, and A.V. Sreejith

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We propose One-counter Positive Negative Inference (OPNI), a passive learning algorithm for deterministic real-time one-counter automata (DROCA). Inspired by the RPNI algorithm for regular languages, OPNI constructs a DROCA consistent with any given valid sample set. We further present a semi-algorithm for active learning of DROCA using OPNI, and provide an implementation of the approach. Our experimental results demonstrate that this approach scales more effectively than existing state-of-the-art algorithms. We also evaluate the performance of the proposed approach for learning visibly one-counter automata.
Cite as

Shibashis Guha, Anirban Majumdar, Prince Mathew, and A.V. Sreejith. Scalable Learning of One-Counter Automata via State-Merging Algorithms. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 35:1-35:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{guha_et_al:LIPIcs.FSTTCS.2025.35,
  author =	{Guha, Shibashis and Majumdar, Anirban and Mathew, Prince and Sreejith, A.V.},
  title =	{{Scalable Learning of One-Counter Automata via State-Merging Algorithms}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{35:1--35:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.35},
  URN =		{urn:nbn:de:0030-drops-251168},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.35},
  annote =	{Keywords: active learning, passive learning, one-counter automata, RPNI}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.31
Games with ω-Automatic Preference Relations

Authors: Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
This paper investigates Nash equilibria (NEs) in multi-player turn-based games on graphs, where player preferences are modeled as ω-automatic relations via deterministic parity automata. Unlike much of the existing literature, which focuses on specific reward functions, our results apply to any preference relation definable by an ω-automatic relation. We analyze the computational complexity of determining the existence of an NE (possibly under some constraints), verifying whether a given strategy profile forms an NE, and checking whether a specific outcome can be realized by an NE. When a (constrained) NE exists, we show that there always exists one with finite-memory strategies. Finally, we explore fundamental properties of ω-automatic relations and their implications in the existence of equilibria.
Cite as

Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin. Games with ω-Automatic Preference Relations. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bruyere_et_al:LIPIcs.MFCS.2025.31,
  author =	{Bruy\`{e}re, V\'{e}ronique and Grandmont, Christophe and Raskin, Jean-Fran\c{c}ois},
  title =	{{Games with \omega-Automatic Preference Relations}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.31},
  URN =		{urn:nbn:de:0030-drops-241381},
  doi =		{10.4230/LIPIcs.MFCS.2025.31},
  annote =	{Keywords: Games played on graphs, Nash equilibrium, \omega-automatic relations, \omega-recognizable relations, constrained Nash equilibria existence problem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.30
Finding Equilibria: Simpler for Pessimists, Simplest for Optimists

Authors: Léonard Brice, Thomas A. Henzinger, and K. S. Thejaswini

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We consider equilibria in multiplayer stochastic graph games with terminal-node rewards. In such games, Nash equilibria are defined assuming that each player seeks to maximise their expected payoff, ignoring their aversion or tolerance to risk. We therefore study risk-sensitive equilibria (RSEs), where the expected payoff is replaced by a risk measure. A classical risk measure in the literature is the entropic risk measure, where each player has a real valued parameter capturing their risk-averseness. We introduce the extreme risk measure, which corresponds to extreme cases of entropic risk measure, where players are either extreme optimists or extreme pessimists. Under extreme risk measure, every player is an extremist: an extreme optimist perceives their reward as the maximum payoff that can be achieved with positive probability, while an extreme pessimist expects the minimum payoff achievable with positive probability. We argue that the extreme risk measure, especially in multi-player graph based settings, is particularly relevant as they can model several real life instances such as interactions between secure systems and potential security threats, or distributed controls for safety critical systems. We prove that RSEs defined with the extreme risk measure are guaranteed to exist when all rewards are non-negative. Furthermore, we prove that the problem of deciding whether a given game contains an RSE that generates risk measures within specified intervals is decidable and NP-complete for our extreme risk measure, and even PTIME-complete when all players are extreme optimists, while that same problem is undecidable using the entropic risk measure or even the classical expected payoff. This establishes, to our knowledge, the first decidable fragment for equilibria in simple stochastic games without restrictions on strategy types or number of players.
Cite as

Léonard Brice, Thomas A. Henzinger, and K. S. Thejaswini. Finding Equilibria: Simpler for Pessimists, Simplest for Optimists. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{brice_et_al:LIPIcs.MFCS.2025.30,
  author =	{Brice, L\'{e}onard and Henzinger, Thomas A. and Thejaswini, K. S.},
  title =	{{Finding Equilibria: Simpler for Pessimists, Simplest for Optimists}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{30:1--30:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.30},
  URN =		{urn:nbn:de:0030-drops-241371},
  doi =		{10.4230/LIPIcs.MFCS.2025.30},
  annote =	{Keywords: Nash equilibria, stochastic games, graph games, risk-sensitive equilibria}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.12
The Non-Cooperative Rational Synthesis Problem for SPEs and ω-Regular Objectives

Authors: Véronique Bruyère, Jean-François Raskin, Alexis Reynouard, and Marie Van Den Bogaard

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
This paper studies the rational synthesis problem for multi-player games played on graphs when rational players are following subgame perfect equilibria. In these games, one player, the system, declares his strategy upfront, and the other players, composing the environment, then rationally respond by playing strategies forming a subgame perfect equilibrium. We study the complexity of the rational synthesis problem when the players have ω-regular objectives encoded as parity objectives. Our algorithm is based on an encoding into a three-player game with imperfect information, showing that the problem is in 2ExpTime. When the number of environment players is fixed, the problem is in ExpTime and is NP- and coNP-hard. Moreover, for a fixed number of players and reachability objectives, we get a polynomial algorithm.
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Véronique Bruyère, Jean-François Raskin, Alexis Reynouard, and Marie Van Den Bogaard. The Non-Cooperative Rational Synthesis Problem for SPEs and ω-Regular Objectives. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bruyere_et_al:LIPIcs.CONCUR.2025.12,
  author =	{Bruy\`{e}re, V\'{e}ronique and Raskin, Jean-Fran\c{c}ois and Reynouard, Alexis and Van Den Bogaard, Marie},
  title =	{{The Non-Cooperative Rational Synthesis Problem for SPEs and \omega-Regular Objectives}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{12:1--12:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.12},
  URN =		{urn:nbn:de:0030-drops-239622},
  doi =		{10.4230/LIPIcs.CONCUR.2025.12},
  annote =	{Keywords: non-zero-sum games, subgame perfect equilibria, rational synthesis}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2025.14
Pareto Fronts for Compositionally Solving String Diagrams of Parity Games

Authors: Kazuki Watanabe

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract
Open parity games are proposed as a compositional extension of parity games with algebraic operations, forming string diagrams of parity games. A potential application of string diagrams of parity games is to describe a large parity game with a given compositional structure and solve it efficiently as a divide-and-conquer algorithm by exploiting its compositional structure. Building on our recent progress in open Markov decision processes, we introduce Pareto fronts of open parity games, offering a framework for multi-objective solutions. We establish the positional determinacy of open parity games with respect to their Pareto fronts through a novel translation method. Our translation converts an open parity game into a parity game tailored to a given single-objective. Furthermore, we present a simple algorithm for solving open parity games, derived from this translation that allows the application of existing efficient algorithms for parity games. Expanding on this foundation, we develop a compositional algorithm for string diagrams of parity games.
Cite as

Kazuki Watanabe. Pareto Fronts for Compositionally Solving String Diagrams of Parity Games. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{watanabe:LIPIcs.CALCO.2025.14,
  author =	{Watanabe, Kazuki},
  title =	{{Pareto Fronts for Compositionally Solving String Diagrams of Parity Games}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.14},
  URN =		{urn:nbn:de:0030-drops-235734},
  doi =		{10.4230/LIPIcs.CALCO.2025.14},
  annote =	{Keywords: parity game, compositionality, string diagram}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.23
Permissive Equilibria in Multiplayer Reachability Games

Authors: Aline Goeminne and Benjamin Monmege

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
We study multi-strategies in multiplayer reachability games played on finite graphs. A multi-strategy prescribes a set of possible actions, instead of a single action as usual strategies: it represents a set of all strategies that are consistent with it. We aim for profiles of multi-strategies (a multi-strategy per player), where each profile of consistent strategies is a Nash equilibrium, or a subgame perfect equilibrium. The permissiveness of two multi-strategies can be compared with penalties, as already used in the two-player zero-sum setting by Bouyer, Duflot, Markey and Renault [Patricia Bouyer et al., 2009]. We show that we can decide the existence of a multi-strategy profile that is a Nash equilibrium or a subgame perfect equilibrium, while satisfying some upper-bound constraints on the penalties in PSPACE, if the upper-bound penalties are given in unary. The same holds when we search for multi-strategies where certain players are asked to win in at least one play or in all plays.
Cite as

Aline Goeminne and Benjamin Monmege. Permissive Equilibria in Multiplayer Reachability Games. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{goeminne_et_al:LIPIcs.CSL.2025.23,
  author =	{Goeminne, Aline and Monmege, Benjamin},
  title =	{{Permissive Equilibria in Multiplayer Reachability Games}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{23:1--23:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.23},
  URN =		{urn:nbn:de:0030-drops-227801},
  doi =		{10.4230/LIPIcs.CSL.2025.23},
  annote =	{Keywords: multiplayer reachability games, penalties, permissive equilibria}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.14
As Soon as Possible but Rationally

Authors: Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
This paper addresses complexity problems in rational verification and synthesis for multi-player games played on weighted graphs, where the objective of each player is to minimize the cost of reaching a specific set of target vertices. In these games, one player, referred to as the system, declares his strategy upfront. The other players, composing the environment, then rationally make their moves according to their objectives. The rational behavior of these responding players is captured through two models: they opt for strategies that either represent a Nash equilibrium or lead to a play with a Pareto-optimal cost tuple.
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Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin. As Soon as Possible but Rationally. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bruyere_et_al:LIPIcs.CONCUR.2024.14,
  author =	{Bruy\`{e}re, V\'{e}ronique and Grandmont, Christophe and Raskin, Jean-Fran\c{c}ois},
  title =	{{As Soon as Possible but Rationally}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.14},
  URN =		{urn:nbn:de:0030-drops-207869},
  doi =		{10.4230/LIPIcs.CONCUR.2024.14},
  annote =	{Keywords: Games played on graphs, rational verification, rational synthesis, Nash equilibrium, Pareto-optimality, quantitative reachability objectives}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2022.33
Pareto-Rational Verification

Authors: Véronique Bruyère, Jean-François Raskin, and Clément Tamines

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract
We study the rational verification problem which consists in verifying the correctness of a system executing in an environment that is assumed to behave rationally. We consider the model of rationality in which the environment only executes behaviors that are Pareto-optimal with regard to its set of objectives, given the behavior of the system (which is committed in advance of any interaction). We examine two ways of specifying this behavior, first by means of a deterministic Moore machine, and then by lifting its determinism. In the latter case the machine may embed several different behaviors for the system, and the universal rational verification problem aims at verifying that all of them are correct when the environment is rational. For parity objectives, we prove that the Pareto-rational verification problem is co-NP-complete and that its universal version is in PSPACE and both NP-hard and co-NP-hard. For Boolean Büchi objectives, the former problem is Π₂𝖯-complete and the latter is PSPACE-complete. We also study the case where the objectives are expressed using LTL formulas and show that the first problem is PSPACE-complete, and that the second is 2EXPTIME-complete. Both problems are also shown to be fixed-parameter tractable for parity and Boolean Büchi objectives.
Cite as

Véronique Bruyère, Jean-François Raskin, and Clément Tamines. Pareto-Rational Verification. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 33:1-33:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bruyere_et_al:LIPIcs.CONCUR.2022.33,
  author =	{Bruy\`{e}re, V\'{e}ronique and Raskin, Jean-Fran\c{c}ois and Tamines, Cl\'{e}ment},
  title =	{{Pareto-Rational Verification}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{33:1--33:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.33},
  URN =		{urn:nbn:de:0030-drops-170968},
  doi =		{10.4230/LIPIcs.CONCUR.2022.33},
  annote =	{Keywords: Rational verification, Model-checking, Pareto-optimality, \omega-regular objectives}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.25
Time Flies When Looking out of the Window: Timed Games with Window Parity Objectives

Authors: James C. A. Main, Mickael Randour, and Jeremy Sproston

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract
The window mechanism was introduced by Chatterjee et al. to reinforce mean-payoff and total-payoff objectives with time bounds in two-player turn-based games on graphs [Krishnendu Chatterjee et al., 2015]. It has since proved useful in a variety of settings, including parity objectives in games [Véronique Bruyère et al., 2016] and both mean-payoff and parity objectives in Markov decision processes [Thomas Brihaye et al., 2020]. We study window parity objectives in timed automata and timed games: given a bound on the window size, a path satisfies such an objective if, in all states along the path, we see a sufficiently small window in which the smallest priority is even. We show that checking that all time-divergent paths of a timed automaton satisfy such a window parity objective can be done in polynomial space, and that the corresponding timed games can be solved in exponential time. This matches the complexity class of timed parity games, while adding the ability to reason about time bounds. We also consider multi-dimensional objectives and show that the complexity class does not increase. To the best of our knowledge, this is the first study of the window mechanism in a real-time setting.
Cite as

James C. A. Main, Mickael Randour, and Jeremy Sproston. Time Flies When Looking out of the Window: Timed Games with Window Parity Objectives. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{main_et_al:LIPIcs.CONCUR.2021.25,
  author =	{Main, James C. A. and Randour, Mickael and Sproston, Jeremy},
  title =	{{Time Flies When Looking out of the Window: Timed Games with Window Parity Objectives}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{25:1--25:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.25},
  URN =		{urn:nbn:de:0030-drops-144021},
  doi =		{10.4230/LIPIcs.CONCUR.2021.25},
  annote =	{Keywords: Window objectives, timed automata, timed games, parity games}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.27
Stackelberg-Pareto Synthesis

Authors: Véronique Bruyère, Jean-François Raskin, and Clément Tamines

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract
In this paper, we study the framework of two-player Stackelberg games played on graphs in which Player 0 announces a strategy and Player 1 responds rationally with a strategy that is an optimal response. While it is usually assumed that Player 1 has a single objective, we consider here the new setting where he has several. In this context, after responding with his strategy, Player 1 gets a payoff in the form of a vector of Booleans corresponding to his satisfied objectives. Rationality of Player 1 is encoded by the fact that his response must produce a Pareto-optimal payoff given the strategy of Player 0. We study the Stackelberg-Pareto Synthesis problem which asks whether Player 0 can announce a strategy which satisfies his objective, whatever the rational response of Player 1. For games in which objectives are either all parity or all reachability objectives, we show that this problem is fixed-parameter tractable and NEXPTIME-complete. This problem is already NP-complete in the simple case of reachability objectives and graphs that are trees.
Cite as

Véronique Bruyère, Jean-François Raskin, and Clément Tamines. Stackelberg-Pareto Synthesis. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bruyere_et_al:LIPIcs.CONCUR.2021.27,
  author =	{Bruy\`{e}re, V\'{e}ronique and Raskin, Jean-Fran\c{c}ois and Tamines, Cl\'{e}ment},
  title =	{{Stackelberg-Pareto Synthesis}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{27:1--27:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.27},
  URN =		{urn:nbn:de:0030-drops-144040},
  doi =		{10.4230/LIPIcs.CONCUR.2021.27},
  annote =	{Keywords: Stackelberg non-zero sum games played on graphs, synthesis, parity objectives}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2019.13
The Complexity of Subgame Perfect Equilibria in Quantitative Reachability Games

Authors: Thomas Brihaye, Véronique Bruyère, Aline Goeminne, Jean-François Raskin, and Marie van den Bogaard

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

Abstract
We study multiplayer quantitative reachability games played on a finite directed graph, where the objective of each player is to reach his target set of vertices as quickly as possible. Instead of the well-known notion of Nash equilibrium (NE), we focus on the notion of subgame perfect equilibrium (SPE), a refinement of NE well-suited in the framework of games played on graphs. It is known that there always exists an SPE in quantitative reachability games and that the constrained existence problem is decidable. We here prove that this problem is PSPACE-complete. To obtain this result, we propose a new algorithm that iteratively builds a set of constraints characterizing the set of SPE outcomes in quantitative reachability games. This set of constraints is obtained by iterating an operator that reinforces the constraints up to obtaining a fixpoint. With this fixpoint, the set of SPE outcomes can be represented by a finite graph of size at most exponential. A careful inspection of the computation allows us to establish PSPACE membership.
Cite as

Thomas Brihaye, Véronique Bruyère, Aline Goeminne, Jean-François Raskin, and Marie van den Bogaard. The Complexity of Subgame Perfect Equilibria in Quantitative Reachability Games. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{brihaye_et_al:LIPIcs.CONCUR.2019.13,
  author =	{Brihaye, Thomas 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}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{13:1--13:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.13},
  URN =		{urn:nbn:de:0030-drops-109153},
  doi =		{10.4230/LIPIcs.CONCUR.2019.13},
  annote =	{Keywords: multiplayer non-zero-sum games played on graphs, quantitative reachability objectives, subgame perfect equilibria, constrained existence problem}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2019.21
Energy Mean-Payoff Games

Authors: Véronique Bruyère, Quentin Hautem, Mickael Randour, and Jean-François Raskin

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

Abstract
In this paper, we study one-player and two-player energy mean-payoff games. Energy mean-payoff games are games of infinite duration played on a finite graph with edges labeled by 2-dimensional weight vectors. The objective of the first player (the protagonist) is to satisfy an energy objective on the first dimension and a mean-payoff objective on the second dimension. We show that optimal strategies for the first player may require infinite memory while optimal strategies for the second player (the antagonist) do not require memory. In the one-player case (where only the first player has choices), the problem of deciding who is the winner can be solved in polynomial time while for the two-player case we show co-NP membership and we give effective constructions for the infinite-memory optimal strategies of the protagonist.
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Véronique Bruyère, Quentin Hautem, Mickael Randour, and Jean-François Raskin. Energy Mean-Payoff Games. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bruyere_et_al:LIPIcs.CONCUR.2019.21,
  author =	{Bruy\`{e}re, V\'{e}ronique and Hautem, Quentin and Randour, Mickael and Raskin, Jean-Fran\c{c}ois},
  title =	{{Energy Mean-Payoff Games}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.21},
  URN =		{urn:nbn:de:0030-drops-109239},
  doi =		{10.4230/LIPIcs.CONCUR.2019.21},
  annote =	{Keywords: two-player zero-sum games played on graphs, energy and mean-payoff objectives, complexity study and construction of optimal strategies}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2018.29
Parameterized complexity of games with monotonically ordered omega-regular objectives

Authors: Véronique Bruyère, Quentin Hautem, and Jean-François Raskin

Published in: LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

Abstract
In recent years, two-player zero-sum games with multiple objectives have received a lot of interest as a model for the synthesis of complex reactive systems. In this framework, Player 1 wins if he can ensure that all objectives are satisfied against any behavior of Player 2. When this is not possible to satisfy all the objectives at once, an alternative is to use some preorder on the objectives according to which subset of objectives Player 1 wants to satisfy. For example, it is often natural to provide more significance to one objective over another, a situation that can be modelled with lexicographically ordered objectives for instance. Inspired by recent work on concurrent games with multiple omega-regular objectives by Bouyer et al., we investigate in detail turned-based games with monotonically ordered and omega-regular objectives. We study the threshold problem which asks whether player 1 can ensure a payoff greater than or equal to a given threshold w.r.t. a given monotonic preorder. As the number of objectives is usually much smaller than the size of the game graph, we provide a parametric complexity analysis and we show that our threshold problem is in FPT for all monotonic preorders and all classical types of omega-regular objectives. We also provide polynomial time algorithms for Büchi, coBüchi and explicit Muller objectives for a large subclass of monotonic preorders that includes among others the lexicographic preorder. In the particular case of lexicographic preorder, we also study the complexity of computing the values and the memory requirements of optimal strategies.
Cite as

Véronique Bruyère, Quentin Hautem, and Jean-François Raskin. Parameterized complexity of games with monotonically ordered omega-regular objectives. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bruyere_et_al:LIPIcs.CONCUR.2018.29,
  author =	{Bruy\`{e}re, V\'{e}ronique and Hautem, Quentin and Raskin, Jean-Fran\c{c}ois},
  title =	{{Parameterized complexity of games with monotonically ordered omega-regular objectives}},
  booktitle =	{29th International Conference on Concurrency Theory (CONCUR 2018)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-087-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{118},
  editor =	{Schewe, Sven and Zhang, Lijun},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.29},
  URN =		{urn:nbn:de:0030-drops-95673},
  doi =		{10.4230/LIPIcs.CONCUR.2018.29},
  annote =	{Keywords: two-player zero-sum games played on graphs, omega-regular objectives, ordered objectives, parameterized complexity}
}
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