On the synthesis of strategies in infinite games

Thomas, Wolfgang

doi:10.1007/3-540-59042-0_57

Cited by 273 publications

(245 citation statements)

References 21 publications

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“…It was suggested by Wolfgang Thomas [25]. One may consider a nonterminating reactive program as a player in a two person infinite game, the other player being the environment.…”

Section: Introductionmentioning

confidence: 99%

Pushdown processes: Games and model checking

Walukiewicz

1996

Lecture Notes in Computer Science

108

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A pushdown game is a two player perfect information infinite game on a transition graph of a pushdown automaton. A winning condition in such a game is defined in terms of states appearing infinitely often in the play. It is shown that if there is a winning strategy in a pushdown game then there is a winning strategy realized by a pushdown automaton. An EXPTIME procedure for finding a winner in a pushdown game is presented. The procedure is then used to solve the model-checking problem for the pushdown processes and the propositional µ-calculus. The problem is shown to be DEXPTIME-complete.

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“…It was suggested by Wolfgang Thomas [25]. One may consider a nonterminating reactive program as a player in a two person infinite game, the other player being the environment.…”

Section: Introductionmentioning

confidence: 99%

Pushdown processes: Games and model checking

Walukiewicz

1996

Lecture Notes in Computer Science

108

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“…In other words, the compatible states are those from which Input has a winning strategy. The calculation of winning strategy in such safety games, if one exists, by using the controllable predecessors of a set of states U and iterative refinement is standard [19].…”

Section: Interface Automatamentioning

confidence: 99%

Synthesis of Interface Automata

Bhaduri

2005

Automated Technology for Verification and Analysis

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Abstract. We investigate the problem of synthesising an interface automaton R such that P R Q, for given deterministic interface automata P and Q. We show that a solution exists iff P and Q ⊥ are compatible, and the most general solution is given by (P Q ⊥ ) ⊥ , where P ⊥ is the automaton P with inputs and outputs interchanged. We also characterise solutions in terms of winning input strategies in the automaton (P ⊗ Q ⊥ ) ⊥ , and the most general solution in terms of the most permissive winning strategy. We apply the synthesis problem for interfaces to the problem of synthesising converters for mismatched protocols.

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“…The definition of the game solving problem in the framework of timed automata [2] was given by Maler et al [15,3]. In their fundamental work, the decidability of the problem was shown by demonstrating that the standard discrete attractor construction [19] on the region graph suffices to obtain winning strategies. Henzinger and Kopke showed that this construction is theoretically optimal by proving EXPTIME-completeness of the problem [13].…”

Section: Introductionmentioning

confidence: 99%

Combining Symbolic Representations for Solving Timed Games

Ehlers

Mattmüller²,

Peter

2010

Lecture Notes in Computer Science

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Abstract. We present a general approach to combine symbolic state space representations for the discrete and continuous parts in the synthesis of winning strategies for timed reachability games. The combination is based on abstraction refinement where discrete symbolic techniques are used to produce a sequence of abstract timed game automata. After each refinement step, the resulting abstraction is used for computing an under-and an over-approximation of the timed winning states. The key idea is to identify large relevant and irrelevant parts of the precise weakest winning strategy already on coarse, and therefore simple, abstractions. If neither the existence nor nonexistence of a winning strategy can be established in the approximations, we use them to guide the refinement process. Based on a prototype that combines binary decision diagrams [7,9] and difference bound matrices [5], we experimentally evaluate the technique on standard benchmarks from timed controller synthesis. The results clearly demonstrate the potential of the new approach concerning running time and memory consumption compared to the classical on-the-fly algorithm implemented in Uppaal-Tiga [10,4].

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On the synthesis of strategies in infinite games

Cited by 273 publications

References 21 publications

Pushdown processes: Games and model checking

Pushdown processes: Games and model checking

Synthesis of Interface Automata

Combining Symbolic Representations for Solving Timed Games

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