A Sub-quadratic Algorithm for Conjunctive and Disjunctive Boolean Equation Systems

摘要

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.