Partial-Order Reduction in Symbolic State Space Exploration

State space explosion is a fundamental obstacle in formal veri cation of designs and protocols. Several techniques for combating this problem have emerged in the past few years, among which two are signi cant: partialorder reductions and symbolic state space search. In asynchronous systems, interleavings of independent concurrent events are equivalent, and only a representative interleaving needs to be explored to verify local properties. Partialorder methods exploit this redundancy and visit only a subset of the reachable states. Symbolic techniques, on the other hand, capture the transition relation of a system and the set of reachable states as boolean functions. In many cases, these functions can be represented compactly using binary decision diagrams (BDDs). Traditionally, the two techniques have been practiced by two di erent schools|partial-order methods with enumerative depthrst search for the analysis of asynchronous network protocols, and symbolic breadthrst search for the analysis of synchronous hardware designs. We combine both approaches and develop a method for using partial-order reduction techniques in symbolic BDD-based invariant checking. We present theoretical results to prove the correctness of the method, and experimental results to demonstrate its e cacy.