Parallel Model Checking for LTL, CTL∗, and L2μ

Abstract

We describe a parallel model-checking algorithm for the fragment of the μ-calculus that allows one alternation of minimal and maximal fixed-point operators. This fragment is also known as L2μ. Since LTL and CTL∗ can be encoded in this fragment, we obtain parallel model checking algorithms for practically important temporal logics.Our solution is based on a characterization of this problem in terms of two player games. We exhibit the structure of their game graphs and show that we can iteratively work with game graphs that have the same special structure as the ones obtained for L1μ-formulae. Since good parallel algorithms for colouring game-graphs for L1μ-formulae exist, it is straightforward to implement this algorithm in parallel and good run-time results can be expected.