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Decidability of Zenoness, Token Liveness and Boundedness for DenseTimed Petri Nets

Summary: Decidability of Zenoness, Token Liveness and
Boundedness for Dense­Timed Petri Nets
Parosh Abdulla 1 , Pritha Mahata 1 , and Richard Mayr 2
1 Uppsala University, Sweden
2 Albert­Ludwigs­University Freiburg, Germany
E­mail: fparosh,prithag@it.uu.se,mayrri@informatik.uni­freiburg.de
Abstract. We consider Timed Petri Nets (TPNs) : extensions of Petri nets in
which each token is equipped with a real­valued clock. We consider the following
three verification problems for TPN.
(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 bounded­
ness where also dead tokens are considered. We show undecidability of semantic


Source: Abdulla, Parosh Aziz - Department of Information Technology, Uppsala Universitet


Collections: Computer Technologies and Information Sciences