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The Complexity of Synthesizing Uniform Strategies

Bastien Maubert 1 Sophie Pinchinat 1 Laura Bozzelli 2 
1 S4 - System synthesis and supervision, scenarios
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : We investigate uniformity properties of strategies. These properties involve sets of plays in order to express useful constraints on strategies that are not \mu-calculus definable. Typically, we can state that a strategy is observation-based. We propose a formal language to specify uniformity properties, interpreted over two-player turn-based arenas equipped with a binary relation between plays. This way, we capture e.g. games with winning conditions expressible in epistemic temporal logic, whose underlying equivalence relation between plays reflects the observational capabilities of agents (for example, synchronous perfect recall). Our framework naturally generalizes many other situations from the literature. We establish that the problem of synthesizing strategies under uniformity constraints based on regular binary relations between plays is non-elementary complete.
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Submitted on : Monday, December 29, 2014 - 10:12:11 AM
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Bastien Maubert, Sophie Pinchinat, Laura Bozzelli. The Complexity of Synthesizing Uniform Strategies. 1st International Workshop on Strategic Reasoning, 2013, Mar 2013, Rome, Italy. pp.8, ⟨10.4204/EPTCS.112.17⟩. ⟨hal-01098745⟩



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