Effective strategies for enumeration games

We study the existence of effective winning strategies in certain infinite games, so called enumeration games. Originally, these were introduced by Lachlan (1970) in his study of the lattice of recursively enumerable sets. We argue that they provide a general and interesting framework for computable games and may also be well suited for modelling reactive systems. Our results are obtained by reductions of enumeration games to regular games. For the latter effective winning strategies exist by a classical result of Buechi and Landweber. This provides more perspicuous proofs for several of Lachlan\u27s results as well as a key for new results. It also shows a way of how strategies for regular games can be scaled up such that they apply to much more general games

Effective Strategies for Enumeration Games

We study the existence of effective winning strategies in certain infinite games, so called enumeration games. Originally, these were introduced by Lachlan (1970) in his study of the lattice of recursively enumerable sets. We argue that they provide a general and interesting framework for computable games and may also be well suited for modelling reactive systems. Our results are obtained by reductions of enumeration games to regular games. For the latter effective winning strategies exist by a classical result of Buchi and Landweber. This provides more perspicuous proofs for several of Lachlan's results as well as a key for new results. It also shows a way of how strategies for regular games can be scaled up such that they apply to much more general games. 1 Introduction Infinite games have been studied for a long time in many areas of mathematical logic. In recent years they also appeared in computer science as a framework for modelling reactive systems (see [Tho95] for a recent sur..