Characterizing Stable Inequalities of Petri Nets

  • Marvin TriebelEmail author
  • Jan Sürmeli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9115)


One way to express correctness of a Petri net \(N\) is to specify a linear inequality \(U\), requiring each reachable marking of \(N\) to satisfy \(U\). A linear inequality \(U\) is stable if it is preserved along steps. If \(U\) is stable, then verifying correctness reduces to checking \(U\) in the initial marking of \(N\). In this paper, we characterize classes of stable linear inequalities of a given Petri net by means of structural properties. Thereby, we generalize classical results on traps, co-traps, and invariants. We show how to decide stability of a given inequality. For a certain class of inequalities, we present a polynomial time decision procedure.


Petri net analysis Inductive invariants Linear inequalities Stable properties Traps Co-traps Invariants 


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institut für InformatikHumboldt-Universität zu BerlinBerlinGermany

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