Showing papers by "Jean-François Raskin published in 2018"
09 Jul 2018
TL;DR: This paper studies the rational synthesis problem for turn-based multiplayer non zero-sum games played on finite graphs for omega-regular objectives and shows that this problem is ExpTime-C for parity objectives in the two-player case (even if both players are imperfectly informed) and undecidable for more than 2 players.
Abstract: In this paper, we study the rational synthesis problem for turn-based multiplayer non zero-sum games played on finite graphs for omega-regular objectives. Rationality is formalized by the concept of Nash equilibrium (NE). Contrary to previous works, we consider here the more general and more practically relevant case where players are imperfectly informed. In sharp contrast with the perfect information case, NE are not guaranteed to exist in this more general setting. This motivates the study of the NE existence problem. We show that this problem is ExpTime-C for parity objectives in the two-player case (even if both players are imperfectly informed) and undecidable for more than 2 players. We then study the rational synthesis problem and show that the problem is also ExpTime-C for two imperfectly informed players and undecidable for more than 3 players. As the rational synthesis problem considers a system (Player 0) playing against a rational environment (composed of k players), we also consider the natural case where only Player 0 is imperfectly informed about the state of the environment (and the environment is considered as perfectly informed). In this case, we show that the ExpTime-C result holds when k is arbitrary but fixed. We also analyse the complexity when k is part of the input.
19 citations
07 Sep 2018
TL;DR: In this article, the authors studied the constrained existence problem for weak subgame perfect equilibria (weak SPE), a refinement of weak SPE, where players who deviate can only use the subclass of strategies that differ from the original one on a finite number of histories.
Abstract: We study multiplayer turn-based games played on a finite directed graph such that each player aims at satisfying an ω-regular Boolean objective. Instead of the well-known notions of Nash equilibrium (NE) and subgame perfect equilibrium (SPE), we focus on the recent notion of weak subgame perfect equilibrium (weak SPE), a refinement of SPE. In this setting, players who deviate can only use the subclass of strategies that differ from the original one on a finite number of histories. We are interested in the constrained existence problem for weak SPEs. We provide a complete characterization of the computational complexity of this problem: it is P-complete for Explicit Muller objectives, NP-complete for Co-Buchi, Parity, Muller, Rabin, and Streett objectives, and PSPACE-complete for Reachability and Safety objectives (we only prove NP-membership for Buchi objectives). We also show that the constrained existence problem is fixed parameter tractable and is polynomial when the number of players is fixed. All these results are based on a fine-grained analysis of a fixpoint algorithm that computes the set of possible payoff profiles underlying weak SPEs.
10 citations
TL;DR: The algorithmic, closure and expressiveness properties of VPT are studied to define transformations from nested words to words and can be seen as a subclass of pushdown transducers.
7 citations
TL;DR: It is shown that, in sharp contrast to the classical mean-payoff objectives, some of the window mean- payoff objectives are decidable in games with partial observation.
Abstract: Mean-payoff games (MPGs) are infinite duration two-player zero-sum games played on weighted graphs. Under the hypothesis of perfect information, they admit memoryless optimal strategies for both players and can be solved in Open image in new window . MPGs are suitable quantitative models for open reactive systems. However, in this context the assumption of perfect information is not always realistic. For the partial-observation case, the problem that asks if the first player has an observation-based winning strategy that enforces a given threshold on the mean-payoff, is undecidable. In this paper, we study the window mean-payoff objectives introduced recently as an alternative to the classical mean-payoff objectives. We show that, in sharp contrast to the classical mean-payoff objectives, some of the window mean-payoff objectives are decidable in games with partial-observation.
7 citations
10 Sep 2018
TL;DR: A logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid is introduced, and it is directly obtained that these classical properties can be decided in PTime.
Abstract: We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric, and we provide sufficient conditions on the predicates under which the model-checking problem is decidable. We then consider three particular automata models (finite automata, transducers and automata weighted by integers – sum-automata –) and instantiate the generic logic for each of them. We give tight complexity results for the three logics and the model-checking problem, depending on whether the formula is fixed or not. We study the expressiveness of our logics by expressing classical structural patterns characterising for instance finite ambiguity and polynomial ambiguity in the case of finite automata, determinisability and finite-valuedness in the case of transducers and sum-automata. Consequently to our complexity results, we directly obtain that these classical properties can be decided in PTime.
7 citations
01 Jan 2018
TL;DR: The unified view is based on the notion of region algebras together with appropriate generalizations of the modal \(\mu\)-calculus, which provides a unified approach for formal reasoning about systems that is applicable to many different classes of systems and properties.
Abstract: We consider symbolic model checking as a general procedure to compute fixed points on general lattices. We show that this view provides a unified approach for formal reasoning about systems that is applicable to many different classes of systems and properties. Our unified view is based on the notion of region algebras together with appropriate generalizations of the modal \(\mu\)-calculus. We show applications of our general approach to problems in infinite-state verification, reactive synthesis, and the analysis of probabilistic systems.
4 citations
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TL;DR: A natural representation of boundedness games yields coNP-completeness, whereas the safety games are undecidable; a general characterizations of which player can win such games are provided.
Abstract: We introduce and study Minkowski games. These are two-player games, where the players take turns to choose positions in R We provide some general characterizations of which player can win such games and explore the computational complexity of the associated decision problems. A natural representation of boundedness games yields coNP-completeness, whereas the safety games are undecidable.
4 citations
TL;DR: In this article, the authors considered the constrained existence problem for weak subgame perfect equilibria (weak SPE), a refinement of weak SPE, where players who deviate can only use the subclass of strategies that differ from the original one on a finite number of histories.
Abstract: We study multiplayer turn-based games played on a finite directed graph such that each player aims at satisfying an omega-regular Boolean objective. Instead of the well-known notions of Nash equilibrium (NE) and subgame perfect equilibrium (SPE), we focus on the recent notion of weak subgame perfect equilibrium (weak SPE), a refinement of SPE. In this setting, players who deviate can only use the subclass of strategies that differ from the original one on a finite number of histories. We are interested in the constrained existence problem for weak SPEs. We provide a complete characterization of the computational complexity of this problem: it is P-complete for Explicit Muller objectives, NP-complete for Co-Buchi, Parity, Muller, Rabin, and Streett objectives, and PSPACE-complete for Reachability and Safety objectives (we only prove NP-membership for Buchi objectives). We also show that the constrained existence problem is fixed parameter tractable and is polynomial when the number of players is fixed. All these results are based on a fine analysis of a fixpoint algorithm that computes the set of possible payoff profiles underlying weak SPEs.
3 citations
Posted Content•
TL;DR: In this article, the maximal uniform chain is proposed as the desired dominance-based rationality concept in safety/reachability games, where the goal is to recover a satisfactory rationality notion based on dominance in such games.
Abstract: Admissible strategies, i.e. those that are not dominated by any other strategy, are a typical rationality notion in game theory. In many classes of games this is justified by results showing that any strategy is admissible or dominated by an admissible strategy. However, in games played on finite graphs with quantitative objectives (as used for reactive synthesis), this is not the case.
We consider increasing chains of strategies instead to recover a satisfactory rationality notion based on dominance in such games. We start with some order-theoretic considerations establishing sufficient criteria for this to work. We then turn our attention to generalised safety/reachability games as a particular application. We propose the notion of maximal uniform chain as the desired dominance-based rationality concept in these games. Decidability of some fundamental questions about uniform chains is established.
1 citations
Posted Content•
TL;DR: In this article, a logic to express structural properties of automata with string inputs and outputs in some monoid is introduced, and sufficient conditions on the predicates under which the model-checking problem is decidable.
Abstract: We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric, and we provide sufficient conditions on the predicates under which the model-checking problem is decidable. We then consider three particular automata models (finite automata, transducers and automata weighted by integers -- sum-automata --) and instantiate the generic logic for each of them. We give tight complexity results for the three logics and the model-checking problem, depending on whether the formula is fixed or not. We study the expressiveness of our logics by expressing classical structural patterns characterising for instance finite ambiguity and polynomial ambiguity in the case of finite automata, determinisability and finite-valuedness in the case of transducers and sum-automata. Consequently to our complexity results, we directly obtain that these classical properties can be decided in PTIME.