The Complexity of Synthesizing Uniform Strategies

Bastien Maubert
Sophie Pinchinat
Laura Bozzelli

We investigate uniformity properties of strategies. These properties involve sets of plays in order to express useful constraints on strategies that are not μ-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.

In Fabio Mogavero, Aniello Murano and Moshe Y. Vardi: Proceedings 1st International Workshop on Strategic Reasoning (SR 2013), Rome, Italy, March 16-17, 2013, Electronic Proceedings in Theoretical Computer Science 112, pp. 115–122.
Published: 1st March 2013.

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