A lattice theory for solving games of imperfect information
Martin De Wulf,Laurent Doyen,Jean-François Raskin +2 more
- pp 153-168
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In this article, a fixed point theory is proposed to solve games of imperfect information, which is defined on the lattice of antichains of sets of states and does not involve determinization.Abstract:
In this paper, we propose a fixed point theory to solve games of imperfect information. The fixed point theory is defined on the lattice of antichains of sets of states. Contrary to the classical solution proposed by Reif [Rei84], our new solution does not involve determinization. As a consequence, it is readily applicable to classes of systems that do not admit determinization. Notable examples of such systems are timed and hybrid automata. As an application, we show that the discrete control problem for games of imperfect information defined by rectangular automata is decidable. This result extends a result by Henzinger and Kopke in [HK99].read more
Citations
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Journal ArticleDOI
Algorithms for Omega-Regular Games with Imperfect Information
TL;DR: An algorithm for computing the set of states from which a player can win with probability 1 with a randomized observation-based strategy for a Buechi objective is given and it is shown that these algorithms are optimal by proving matching lower bounds.
Book ChapterDOI
Antichains: a new algorithm for checking universality of finite automata
TL;DR: A new algorithm for checking the universality of nondeterministic finite automata, which computes the least fixed point of a monotone function on the lattice of antichains of state sets and evaluates the performance of this algorithm experimentally using the random automaton model recently proposed by Tabakov and Vardi.
Book ChapterDOI
Algorithms for omega-regular games with imperfect information
TL;DR: A fixed-point algorithm for computing the set of states from which a player can win with a deterministic observation-based strategy for any omega-regular objective is given and it is shown that these algorithms are optimal by proving matching lower bounds.
Book ChapterDOI
Qualitative analysis of partially-observable Markov decision processes
TL;DR: This work presents a complete picture of the computational complexity of the qualitative analysis problem for POMDPs with parity objectives and its subclasses: safety, reachability, Buchi, and coBuchi objectives and establishes several upper and lower bounds that were not known in the literature.
Journal ArticleDOI
Partial-Observation Stochastic Games: How to Win when Belief Fails
TL;DR: In this paper, the authors consider reachability objectives where the first player tries to ensure a target state to be visited almost-surely or positively (i.e., with probability 1) or positively, no matter the strategy of the second player.
References
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The algorithmic analysis of hybrid systems
Rajeev Alur,Costas Courcoubetis,Nicolas Halbwachs,Thomas A. Henzinger,Pei Ho,Xavier Nicollin,Alfredo Olivero,Joseph Sifakis,Sergio Yovine +8 more
TL;DR: A general framework for the formal specification and algorithmic analysis of hybrid systems is presented, which considers symbolic model-checking and minimization procedures that are based on the reachability analysis of an infinite state space.
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Alternating-time temporal logic
TL;DR: This work introduces a third, more general variety of temporal logic: alternating-time temporal logic, which offers selective quantification over those paths that are possible outcomes of games, such as the game in which the system and the environment alternate moves.
Proceedings ArticleDOI
Alternating-time temporal logic
TL;DR: This work introduces a third, more general variety of temporal logic: alternating-time temporal logic offers selective quantification over those paths that are possible outcomes of games, such as the game in which the system and the environment alternate moves.