Uniform Strategies

We consider turn-based game arenas for which we investigate uniformity properties of strategies. These properties involve bundles of plays, that arise from some semantical motive. Typically, we can represent constraints on allowed strategies, such as being observation-based. We propose a formal language to specify uniformity properties and demonstrate its relevance by rephrasing various known problems from the literature. Note that the ability to correlate different plays cannot be achieved by any branching-time logic if not equipped with an additional modality, so-called R in this contribution. 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 bundles of plays rely on any binary relation definable by a finite state transducer. This solution yields a non-elementary procedure.Comment: (2012

Computations by fly-automata beyond monadic second-order logic

We present logically based methods for constructing XP and FPT graph algorithms, parametrized by tree-width or clique-width. We will use fly-automata introduced in a previous article. They make possible to check properties that are not monadic second-order expressible because their states may include counters, so that their sets of states may be infinite. We equip these automata with output functions, so that they can compute values associated with terms or graphs. Rather than new algorithmic results we present tools for constructing easily certain dynamic programming algorithms by combining predefined automata for basic functions and properties.Comment: Accepted for publication in Theoretical Computer Scienc