McNaughton games and extracting strategies for concurrent programs

Abstract

Nerode et al. [ 131 showed that a correct concurrent program can be viewed as a winning strategy in a suitably defined two player game played between the Programmer and the Computer in which the program specification is defined by the rules of the game together with the winning condition. This gives rise to the question as to whether there are useful algorithms to extract (provably) winning strategies in these games, which then yield (provably correct) concurrent programs. Now these games can be described in Rabin’s S2S, the monadic second-order theory of two successors. Decision procedures for the latter show that such algorithms exist. But past available decision methods were too cumbersome to use, even in simple cases. Successively simpler game-based decision procedures for S2S were provided by [5,19,20]. In 1993, based on these papers, McNaughton [8] introduced a class of two player infinite games which are played on a finite graph and have an especially lucid decision procedure for extraction of winning strategies. The games considered in [ 131 can be viewed as a slight variant of Bi.ichi-Landweber games [2]. We give clean algorithms for the equivalence of McNaughton games and Bi.ichi-Landweber games. This allows the McNaughton algorithm to be used to extract (provably) winning strategies, and therefore (verifiably correct) concurrent programs via the Nerode-Yakbnis-Yakhnis paradigm.