Symbolic Representation of Upward-Closed Sets

Abstract. The control state reachability problem is decidable for well-structured infinite-state systems like unbounded Petri Nets, Vector Addition Systems, Lossy Petri Nets, and Broadcast Protocols. An abstract algorithm that solves the problem is given in [ACJT96,FS99]. The algorithm computes the closure of the predecessor operator w.r.t. a given upward-closed set of target states. When applied to this class of verification problems, traditional (infinite-state) symbolic model checkers suffer from the state explosion problem even for very small examples. We provide BDD-like data structures to represent in a compact way collections of upwards closed sets over numerical domains. This way, we turn the abstract algorithm of [ACJT96,FS99] into a practical method. Preliminary experimental results indicate the potential usefulness of our method