Global Caching for the Alternation-free μ-Calculus

We present a sound, complete, and optimal single-pass tableau algorithm for the alternation-free μ-calculus. The algorithm supports global caching with intermediate propagation and runs in time 2O(n). In game-theoretic terms, our algorithm integrates the steps for constructing and solving the Büchi game arising from the input tableau into a single procedure; this is done onthe-fly, i.e. may terminate before the game has been fully constructed. This suggests a slogan to the effect that global caching = game solving on-the-fly. A prototypical implementation shows promising initial results. 1998 ACM Subject Classification F.4.1 Mathematical Logic Temporal Logic