The Complexity of Synthesizing Uniform Strategies

Abstract

We investigate uniformity properties of strategies. These properties involve sets of plays in ord er 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 equip ped 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 reflec ts 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 s ynthesizing strategies under uniformity constraints based on regular binary relations between plays is non-elementary complete.