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Issue title: Special Issue of Selected Papers from Petri Nets 2015
Guest editors: Raymond Devillers, Antti Valmari and Wojciech Penczek
Article type: Research Article
Authors: Triebel, Marvin* | Sürmeli, Jan†
Affiliations: Department of Computer Science, Humboldt-Universität zu Berlin, Germany, triebel@hu-berlin.de, suermeli@hu-berlin.de
Note: [*] Research partially funded by the German Research Foundation (DFG) under grant agreement GRK 1651
Note: [†] Research partially funded by the German Research Foundation (DFG) under grant agreement WE 4891/1-1. Address for correspondence: Department of Computer Science, Humboldt-Universität zu Berlin, Germany
Abstract: 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. 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. Furthermore, we show that stability is a local property and exploit this for the analysis of asynchronously interacting open net structures. Finally, we study the summation of inequalities as means of deriving valid inequalities.
Keywords: Petri net analysis, inductive invariants, linear inequalities, stable properties, traps, co-traps, invariants
DOI: 10.3233/FI-2016-1374
Journal: Fundamenta Informaticae, vol. 146, no. 1, pp. 1-34, 2016
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