Abstract

We study the complexity of several standard problems for 1-safe Petri nets and some of its subclasses. We prove that reachability, liveness, and deadlock are all PSPACE-complete for 1-safe nets. We also prove that deadlock is NP-complete for free-choice nets and for 1-safe free-choice nets. Finally, we prove that for arbitrary Petri nets, deadlock is equivalent to reachability and liveness. This paper is to be presented at FST&TCS 13, Foundations of Software Technology & Theoretical Computer Science, to be held 1517 December 1993, in Bombay, India. A version of the paper with most proofs omitted is to appear in the proceedings. 1 Introduction Petri nets are one of the oldest and most studied formalisms for the investigation of concurrency [33]. Shortly after the birth of complexity theory, Jones, Landweber, and Lien studied in their classical paper [24] the complexity of several fundamental problems for Place/Transition nets (called in [24] just Petri nets). Some years later, Howell,...

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