4 Search Results for "Maubert, Bastien"

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.CSL.2025.10
The Complexity of Second-Order HyperLTL

Authors: Hadar Frenkel and Martin Zimmermann

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

Abstract
We determine the complexity of second-order HyperLTL satisfiability, finite-state satisfiability, and model-checking: All three are equivalent to truth in third-order arithmetic. We also consider two fragments of second-order HyperLTL that have been introduced with the aim to facilitate effective model-checking by restricting the sets one can quantify over. The first one restricts second-order quantification to smallest/largest sets that satisfy a guard while the second one restricts second-order quantification further to least fixed points of (first-order) HyperLTL definable functions. All three problems for the first fragment are still equivalent to truth in third-order arithmetic while satisfiability for the second fragment is Σ₁¹-complete, i.e., only as hard as for (first-order) HyperLTL and therefore much less complex. Finally, finite-state satisfiability and model-checking are in Σ₂² and are Σ₁¹-hard, and thus also less complex than for full second-order HyperLTL.
Cite as

Hadar Frenkel and Martin Zimmermann. The Complexity of Second-Order HyperLTL. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{frenkel_et_al:LIPIcs.CSL.2025.10,
  author =	{Frenkel, Hadar and Zimmermann, Martin},
  title =	{{The Complexity of Second-Order HyperLTL}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{10:1--10:23},
  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.2025.10},
  URN =		{urn:nbn:de:0030-drops-227679},
  doi =		{10.4230/LIPIcs.CSL.2025.10},
  annote =	{Keywords: HyperLTL, Satisfiability, Model-checking}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.23
Quantifying Bounds in Strategy Logic

Authors: Nathanaël Fijalkow, Bastien Maubert, Aniello Murano, and Sasha Rubin

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Program synthesis constructs programs from specifications in an automated way. Strategy Logic (SL) is a powerful and versatile specification language whose goal is to give theoretical foundations for program synthesis in a multi-agent setting. One limitation of Strategy Logic is that it is purely qualitative. For instance it cannot specify quantitative properties of executions such as "every request is quickly granted", or quantitative properties of trees such as "most executions of the system terminate". In this work, we extend Strategy Logic to include quantitative aspects in a way that can express bounds on "how quickly" and "how many". We define Prompt Strategy Logic, which encompasses Prompt LTL (itself an extension of LTL with a prompt eventuality temporal operator), and we define Bounded-Outcome Strategy Logic which has a bounded quantifier on paths. We supply a general technique, based on the study of automata with counters, that solves the model-checking problems for both these logics.
Cite as

Nathanaël Fijalkow, Bastien Maubert, Aniello Murano, and Sasha Rubin. Quantifying Bounds in Strategy Logic. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 23:1-23:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{fijalkow_et_al:LIPIcs.CSL.2018.23,
  author =	{Fijalkow, Nathana\"{e}l and Maubert, Bastien and Murano, Aniello and Rubin, Sasha},
  title =	{{Quantifying Bounds in Strategy Logic}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{23:1--23:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.23},
  URN =		{urn:nbn:de:0030-drops-96901},
  doi =		{10.4230/LIPIcs.CSL.2018.23},
  annote =	{Keywords: Prompt LTL, Strategy Logic, Model checking, Automata with counters}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2013.287
Jumping Automata for Uniform Strategies

Authors: Bastien Maubert and Sophie Pinchinat

Published in: LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)

Abstract
The concept of uniform strategies has recently been proposed as a relevant notion in game theory for computer science. It relies on properties involving sets of plays in two-player turn-based arenas equipped with a binary relation between plays. Among the two notions of fully-uniform and strictly-uniform strategies, we focus on the latter, less explored. We present a language that extends CTL^* with a quantifier over all related plays, which enables to express a rich class of uniformity constraints on strategies. We show that the existence of a uniform strategy is equivalent to the language non-emptiness of a jumping tree automaton. While the existence of a uniform strategy is undecidable for rational binary relations, restricting to ecognizable relations yields a 2EXPTIME-complete complexity, and still captures a class of two-player imperfect-information games with epistemic temporal objectives. This result relies on a translation from jumping tree automata with recognizable relations to two-way tree automata.
Cite as

Bastien Maubert and Sophie Pinchinat. Jumping Automata for Uniform Strategies. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 287-298, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

Copy BibTex To Clipboard

@InProceedings{maubert_et_al:LIPIcs.FSTTCS.2013.287,
  author =	{Maubert, Bastien and Pinchinat, Sophie},
  title =	{{Jumping Automata for Uniform Strategies}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{287--298},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Seth, Anil and Vishnoi, Nisheeth K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.287},
  URN =		{urn:nbn:de:0030-drops-43801},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.287},
  annote =	{Keywords: Games, Imperfect information, Uniform strategies, Jumping automata}
}
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