Decidability of Zenoness, Syntactic Boundedness and Token-Liveness for Dense-Timed Petri Nets

Abstract

We consider Timed Petri Nets (TPNs) : extensions of Petri nets in which each token is equipped with a real-valued clock. We consider the following three verification problems for TPNs. (i) Zenoness: whether there is an infinite computation from a given marking which takes only a finite amount of time. We show decidability of zenoness for TPNs, thus solving an open problem from [dFERA00]. (ii) Token Liveness: whether a token is alive in a marking, i.e., whether there is a computation from the marking which eventually consumes the token.We show decidability of the problem by reducing it to the coverability problem,which is decidable for TPNs. (iii)Boundedness: whether the size of the reachable markings is bounded. We consider two versions of the problem; namely semantic boundedness where only live tokens are taken into consideration in the markings,and syntactic boundedness where also dead tokens are considered. We show undecidability of semantic boundedness, while we prove that syntactic boundedness is decidable through an extension of the Karp-Miller algorithm.