The downward-closure of Petri net languages

Abstract

We show that the downward-closure of a Petri net language is effectively computable. This is mainly done by using the notions defined for showing decidability of the reachability problem of Petri nets. In particular, we rely on Lambert's construction of marked graph transition sequences - special instances of coverability graphs that allow us to extract constructively the simple regular expression corresponding to the downward-closure. We also consider the remaining language types for Petri nets common in the literature. For all of them, we provide algorithms that compute the simple regular expressions of their downward-closure. As application, we outline an algorithm to automatically analyse the stability of a system against attacks from a malicious environment. © 2010 Springer-Verlag Berlin Heidelberg.