Tomiji Hisamura

POC net, a subclass of Petri nets, and its application to timed Petri nets

Abstract Liveness is one of the most important properties of the Petri net analysis. This property is concerned with a capability for firing of transitions. On the other hand, place-liveness is another notion related to liveness, which is concerned with a capability for having tokens in places. Concerning these liveness and place-liveness problems, this paper suggests a new subclass of Petri net, ‘POC nets’, as a superclass of AC nets and DC nets. For this subclass, the equivalence between liveness and place-liveness is shown and a sufficient condition for liveness for this POC net is derived. Then the results are extended to liveness problem of timed Petri nets which have transitions with finite firing durations and the earliest firing rule. Although liveness of a (non-timed) Petri net is neither necessary nor sufficient condition for liveness of a timed Petri net, it is shown that liveness is preserved if the net has POC structure. Furthermore, it is pointed out that if a POC net satisfies some addition...

Minimal time reachability problem of some subclasses of timed Petri nets

Timed Petri net is an effective tool to evaluate discrete event systems. This paper treats the reachability problem of timed Petri nets. The problem aims to find the firing sequence which drives the initial marking M/sub 0/ to the target marking M/sub f/ in minimal execution time. First, we consider the subclass in which non-delayed sequence gives the optimal solution. Then, an algorithm is proposed to solve the minimal time reachability problem of timed state machines.