Combining symbolic and partial order methods for model checking 1-safe Petri nets

摘要

In this work, methods are presented for model checking finite state asynchronous systems, more specifically 1-safe Petri nets, with the aim of alleviating the state explosion problem. Symbolic model checking techniques are used, combined with two partial order semantics known as net unfoldings and processes.We start with net unfoldings and study deadlock and reachability checking problems, using complete finite prefixes of net unfoldings introduced by McMillan. It is shown how these problems can be translated compactly into the problem of finding a stable model of a logic program. This combined with an efficient procedure for finding stable models of a logic program, the Smodels system, provides the basis of a prefix based model checking procedure for deadlock and reachability properties, which is competitive with previously published procedures using prefixes.This work shows that, if the only thing one can assume from a prefix is that it is complete, nested reachability properties are relatively hard. Namely, for several widely used temporal logics which can express a violation of a certain fixed safety property, model checking is PSPACE-complete in the size of the complete finite prefix.A model checking approach is devised for the linear temporal logic LTL-X using complete finite prefixes. The approach makes the complete finite prefix generation formula specific, and the prefix completeness notion application specific. Using these ideas, an LTL-X model checker has been implemented as a variant of a prefix generation algorithm.The use of bounded model checking for asynchronous systems is studied. A method to express the process semantics of a 1-safe Petri net in symbolic form as a set of satisfying truth assignments of a constrained Boolean circuit is presented. In the experiments the BCSat system is used as a circuit satisfiability checker. Another contribution employs logic programs with stable model semantics to develop a new linear size bounded LTL-X model checking translation that can be used with step semantics of 1-safe Petri nets.