Vector Addition Systems with States vs. Petri nets

Florent Avellaneda (1) , Rémi Morin (1)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166

Vector addition systems with states are known to be computationally equivalent to Petri nets. In this paper we compare these two models with respect to the non-branching process semantics based on labeled occurrence nets. We investigate first some basic problems such as reachability, boundedness and covering, when one considers the markings reached by the prefixes of the processes accepted by some vector addition system with states. By means of a new simulation by a Petri net, we prove that these problems are computationally equivalent to the analogous problems for Petri nets. Second, based on some undecidability result from Mazurkiewicz trace theory, we show that one cannot check effectively whether a vector addition system with states is semantically equivalent to some Petri net, even for systems whose prefix-reachable markings are bounded.

Mots clés: Petri nets; vector addition systems with states; non-branching process semantics; reachability; boundedness; covering; Mazurkiewicz traces; universality problem

Domaines: Informatique et langage [cs.CL]

Florent Avellaneda, Rémi Morin. Vector Addition Systems with States vs. Petri nets. 2012. ⟨hal-00686444v1⟩