Using Logic Programs with Stable Model Semantics to Solve Deadlock and Reachability Problems for 1-Safe Petri Nets

Abstract

McMillan has presented a deadlock detection method for Petri nets based on finite complete prefixes (i.e. net unfoldings). The approach transforms the PSPACE-complete deadlock detection problem for a 1-safe Petri net into a potentially exponentially larger NP-complete problem of deadlock detection for a finite complete prefix. McMillan devised a branch-and-bound algorithm for deadlock detection in prefixes. Recently, Melzer and Römer have presented another approach, which is based on solving mixed integer programming problems. In this work it is shown that instead of using mixed integer programming, a constraint-based logic programming framework can be employed, and a linear-size translation from deadlock detection in prefixes into the problem of finding a stable model of a logic program is presented. As a side result also such a translation for solving the reachability problem is devised. Correctness proofs of both the translations are presented. Experimental results are given from an implementation combining the prefix generator of the PEP-tool, the translation, and an implementation of a constraint-based logic programming framework, the smodels system. The experiments show the proposed approach to be quite competitive, when compared to the approaches of McMillan and Melzer/Römer.