A General Notion Of Uniform Strategies

We consider two-player turn-based game arenas for which we investigateuniformity propertiesof strategies. These properties involve sets of plays in order to express useful constraints on strategies that are not μ-calculus definable. Typically, we can representconstraintson allowed strategies, such as being observation-based. We propose a formal language to specify uniformity properties, involving an original modality calledR, meaning "for all related plays". Its semantics is given by some binary relation between plays. We demonstrate the relevance of our approach by rephrasing various known problems from the literature. We also study an automated procedure to synthesize strategies subject to a uniformity property, which strictly extends existing results based on, say standard temporal logics. We exhibit a generic solution for the synthesis problem provided the binary relation that defines the sets of related plays is recognizable by a finite state transducer. This solution yields a nonelementary procedure.