On Liveness of Subclasses of Petri Nets with Permission or Inhibitor Arcs

Abstract

Liveness is one of the most important properties in Petri net analysis, which assures fireability of every transition in the net and avoidance of deadlocks. In this paper we discuss the liveness of extended subclasses of Petri net, i. e. strongly connected marked graphs and strongly connected state machines (SCSM) in which permission or inhibitor arcs are added in restricted structures. The additions of these arcs facilitate modeling of practical discrete event systems by the net. The necessary and/or sufficient conditions for liveness are derived for above subclasses. Then the computational complexities to verify liveness of these nets are discussed and it is shown that liveness of the above subclasses can be verified in deterministic polynomial time by the applications of the obtained criteria.