The downward-closure of petri net languages

Authors:
Peter Habermehl;Roland Meyer;Harro Wimmel
Affiliations:
LIAFA, Paris Diderot University & CNRS;LIAFA, Paris Diderot University & CNRS;Department of Computing Science, University of Rostock
Venue:
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Year:
2010

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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 downwardclosure. As application, we outline an algorithm to automatically analyse the stability of a system against attacks from a malicious environment.