The Downward-Closure of Petri Net Languages

  • Peter Habermehl
  • Roland Meyer
  • Harro Wimmel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6199)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Peter Habermehl
    • 1
  • Roland Meyer
    • 1
  • Harro Wimmel
    • 2
  1. 1.LIAFA, Paris Diderot University & CNRS 
  2. 2.Department of Computing ScienceUniversity of Rostock 

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