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Documents authored by Vandenhove, Pierre


Document
Track B: Automata, Logic, Semantics, and Theory of Programming
How to Play Optimally for Regular Objectives?

Authors: Patricia Bouyer, Nathanaël Fijalkow, Mickael Randour, and Pierre Vandenhove

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
This paper studies two-player zero-sum games played on graphs and makes contributions toward the following question: given an objective, how much memory is required to play optimally for that objective? We study regular objectives, where the goal of one of the two players is that eventually the sequence of colors along the play belongs to some regular language of finite words. We obtain different characterizations of the chromatic memory requirements for such objectives for both players, from which we derive complexity-theoretic statements: deciding whether there exist small memory structures sufficient to play optimally is NP-complete for both players. Some of our characterization results apply to a more general class of objectives: topologically closed and topologically open sets.

Cite as

Patricia Bouyer, Nathanaël Fijalkow, Mickael Randour, and Pierre Vandenhove. How to Play Optimally for Regular Objectives?. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 118:1-118:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bouyer_et_al:LIPIcs.ICALP.2023.118,
  author =	{Bouyer, Patricia and Fijalkow, Nathana\"{e}l and Randour, Mickael and Vandenhove, Pierre},
  title =	{{How to Play Optimally for Regular Objectives?}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{118:1--118:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.118},
  URN =		{urn:nbn:de:0030-drops-181700},
  doi =		{10.4230/LIPIcs.ICALP.2023.118},
  annote =	{Keywords: two-player games on graphs, strategy complexity, regular languages, finite-memory strategies, NP-completeness}
}
Document
Invited Talk
The True Colors of Memory: A Tour of Chromatic-Memory Strategies in Zero-Sum Games on Graphs (Invited Talk)

Authors: Patricia Bouyer, Mickael Randour, and Pierre Vandenhove

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)


Abstract
Two-player turn-based zero-sum games on (finite or infinite) graphs are a central framework in theoretical computer science - notably as a tool for controller synthesis, but also due to their connection with logic and automata theory. A crucial challenge in the field is to understand how complex strategies need to be to play optimally, given a type of game and a winning objective. In this invited contribution, we give a tour of recent advances aiming to characterize games where finite-memory strategies suffice (i.e., using a limited amount of information about the past). We mostly focus on so-called chromatic memory, which is limited to using colors - the basic building blocks of objectives - seen along a play to update itself. Chromatic memory has the advantage of being usable in different game graphs, and the corresponding class of strategies turns out to be of great interest to both the practical and the theoretical sides.

Cite as

Patricia Bouyer, Mickael Randour, and Pierre Vandenhove. The True Colors of Memory: A Tour of Chromatic-Memory Strategies in Zero-Sum Games on Graphs (Invited Talk). In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 3:1-3:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bouyer_et_al:LIPIcs.FSTTCS.2022.3,
  author =	{Bouyer, Patricia and Randour, Mickael and Vandenhove, Pierre},
  title =	{{The True Colors of Memory: A Tour of Chromatic-Memory Strategies in Zero-Sum Games on Graphs}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.3},
  URN =		{urn:nbn:de:0030-drops-173957},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.3},
  annote =	{Keywords: two-player games on graphs, finite-memory strategies, chromatic memory, parity automata, \omega-regularity}
}
Document
Half-Positional Objectives Recognized by Deterministic Büchi Automata

Authors: Patricia Bouyer, Antonio Casares, Mickael Randour, and Pierre Vandenhove

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


Abstract
A central question in the theory of two-player games over graphs is to understand which objectives are half-positional, that is, which are the objectives for which the protagonist does not need memory to implement winning strategies. Objectives for which both players do not need memory have already been characterized (both in finite and infinite graphs); however, less is known about half-positional objectives. In particular, no characterization of half-positionality is known for the central class of ω-regular objectives. In this paper, we characterize objectives recognizable by deterministic Büchi automata (a class of ω-regular objectives) that are half-positional, in both finite and infinite graphs. Our characterization consists of three natural conditions linked to the language-theoretic notion of right congruence. Furthermore, this characterization yields a polynomial-time algorithm to decide half-positionality of an objective recognized by a given deterministic Büchi automaton.

Cite as

Patricia Bouyer, Antonio Casares, Mickael Randour, and Pierre Vandenhove. Half-Positional Objectives Recognized by Deterministic Büchi Automata. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bouyer_et_al:LIPIcs.CONCUR.2022.20,
  author =	{Bouyer, Patricia and Casares, Antonio and Randour, Mickael and Vandenhove, Pierre},
  title =	{{Half-Positional Objectives Recognized by Deterministic B\"{u}chi Automata}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{20:1--20:18},
  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.2022.20},
  URN =		{urn:nbn:de:0030-drops-170833},
  doi =		{10.4230/LIPIcs.CONCUR.2022.20},
  annote =	{Keywords: two-player games on graphs, half-positionality, memoryless optimal strategies, B\"{u}chi automata, \omega-regularity}
}
Document
Characterizing Omega-Regularity Through Finite-Memory Determinacy of Games on Infinite Graphs

Authors: Patricia Bouyer, Mickael Randour, and Pierre Vandenhove

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)


Abstract
We consider zero-sum games on infinite graphs, with objectives specified as sets of infinite words over some alphabet of colors. A well-studied class of objectives is the one of ω-regular objectives, due to its relation to many natural problems in theoretical computer science. We focus on the strategy complexity question: given an objective, how much memory does each player require to play as well as possible? A classical result is that finite-memory strategies suffice for both players when the objective is ω-regular. We show a reciprocal of that statement: when both players can play optimally with a chromatic finite-memory structure (i.e., whose updates can only observe colors) in all infinite game graphs, then the objective must be ω-regular. This provides a game-theoretic characterization of ω-regular objectives, and this characterization can help in obtaining memory bounds. Moreover, a by-product of our characterization is a new one-to-two-player lift: to show that chromatic finite-memory structures suffice to play optimally in two-player games on infinite graphs, it suffices to show it in the simpler case of one-player games on infinite graphs. We illustrate our results with the family of discounted-sum objectives, for which ω-regularity depends on the value of some parameters.

Cite as

Patricia Bouyer, Mickael Randour, and Pierre Vandenhove. Characterizing Omega-Regularity Through Finite-Memory Determinacy of Games on Infinite Graphs. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 16:1-16:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bouyer_et_al:LIPIcs.STACS.2022.16,
  author =	{Bouyer, Patricia and Randour, Mickael and Vandenhove, Pierre},
  title =	{{Characterizing Omega-Regularity Through Finite-Memory Determinacy of Games on Infinite Graphs}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{16:1--16:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.16},
  URN =		{urn:nbn:de:0030-drops-158262},
  doi =		{10.4230/LIPIcs.STACS.2022.16},
  annote =	{Keywords: two-player games on graphs, infinite arenas, finite-memory determinacy, optimal strategies, \omega-regular languages}
}
Document
Arena-Independent Finite-Memory Determinacy in Stochastic Games

Authors: Patricia Bouyer, Youssouf Oualhadj, Mickael Randour, and Pierre Vandenhove

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


Abstract
We study stochastic zero-sum games on graphs, which are prevalent tools to model decision-making in presence of an antagonistic opponent in a random environment. In this setting, an important question is the one of strategy complexity: what kinds of strategies are sufficient or required to play optimally (e.g., randomization or memory requirements)? Our contributions further the understanding of arena-independent finite-memory (AIFM) determinacy, i.e., the study of objectives for which memory is needed, but in a way that only depends on limited parameters of the game graphs. First, we show that objectives for which pure AIFM strategies suffice to play optimally also admit pure AIFM subgame perfect strategies. Second, we show that we can reduce the study of objectives for which pure AIFM strategies suffice in two-player stochastic games to the easier study of one-player stochastic games (i.e., Markov decision processes). Third, we characterize the sufficiency of AIFM strategies through two intuitive properties of objectives. This work extends a line of research started on deterministic games in [Bouyer et al., 2020] to stochastic ones.

Cite as

Patricia Bouyer, Youssouf Oualhadj, Mickael Randour, and Pierre Vandenhove. Arena-Independent Finite-Memory Determinacy in Stochastic Games. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 26:1-26:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{bouyer_et_al:LIPIcs.CONCUR.2021.26,
  author =	{Bouyer, Patricia and Oualhadj, Youssouf and Randour, Mickael and Vandenhove, Pierre},
  title =	{{Arena-Independent Finite-Memory Determinacy in Stochastic Games}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{26:1--26:18},
  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.2021.26},
  URN =		{urn:nbn:de:0030-drops-144037},
  doi =		{10.4230/LIPIcs.CONCUR.2021.26},
  annote =	{Keywords: two-player games on graphs, stochastic games, Markov decision processes, finite-memory determinacy, optimal strategies}
}
Document
Games Where You Can Play Optimally with Arena-Independent Finite Memory

Authors: Patricia Bouyer, Stéphane Le Roux, Youssouf Oualhadj, Mickael Randour, and Pierre Vandenhove

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)


Abstract
For decades, two-player (antagonistic) games on graphs have been a framework of choice for many important problems in theoretical computer science. A notorious one is controller synthesis, which can be rephrased through the game-theoretic metaphor as the quest for a winning strategy of the system in a game against its antagonistic environment. Depending on the specification, optimal strategies might be simple or quite complex, for example having to use (possibly infinite) memory. Hence, research strives to understand which settings allow for simple strategies. In 2005, Gimbert and Zielonka [Hugo Gimbert and Wieslaw Zielonka, 2005] provided a complete characterization of preference relations (a formal framework to model specifications and game objectives) that admit memoryless optimal strategies for both players. In the last fifteen years however, practical applications have driven the community toward games with complex or multiple objectives, where memory - finite or infinite - is almost always required. Despite much effort, the exact frontiers of the class of preference relations that admit finite-memory optimal strategies still elude us. In this work, we establish a complete characterization of preference relations that admit optimal strategies using arena-independent finite memory, generalizing the work of Gimbert and Zielonka to the finite-memory case. We also prove an equivalent to their celebrated corollary of great practical interest: if both players have optimal (arena-independent-)finite-memory strategies in all one-player games, then it is also the case in all two-player games. Finally, we pinpoint the boundaries of our results with regard to the literature: our work completely covers the case of arena-independent memory (e.g., multiple parity objectives, lower- and upper-bounded energy objectives), and paves the way to the arena-dependent case (e.g., multiple lower-bounded energy objectives).

Cite as

Patricia Bouyer, Stéphane Le Roux, Youssouf Oualhadj, Mickael Randour, and Pierre Vandenhove. Games Where You Can Play Optimally with Arena-Independent Finite Memory. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 24:1-24:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bouyer_et_al:LIPIcs.CONCUR.2020.24,
  author =	{Bouyer, Patricia and Le Roux, St\'{e}phane and Oualhadj, Youssouf and Randour, Mickael and Vandenhove, Pierre},
  title =	{{Games Where You Can Play Optimally with Arena-Independent Finite Memory}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{24:1--24:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.24},
  URN =		{urn:nbn:de:0030-drops-128360},
  doi =		{10.4230/LIPIcs.CONCUR.2020.24},
  annote =	{Keywords: two-player games on graphs, finite-memory determinacy, optimal strategies}
}
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