A sub-quadratic algorithm for conjunctive and disjunctive boolean equation systems

We present a new algorithm for conjunctive and disjunctive boolean equation systems which arise frequently in the verification and analysis of finite state concurrent systems. In contrast to the previously known O(e 2) time algorithms, our algorithm computes the solution to such a fixpoint equation system with size e and alternation depth d in O(e log d) time (here d <e). We show the correctness and complexity of the algorithm. We discuss heuristics and describe how the algorithm can be efficiently implemented. The algorithm is compared to a previous solution via experiments on verification examples. Our measurements indicate that the new algorithm makes the verification of a large class of fixpoint expressions more tractable.