Co-Finiteness and Co-Emptiness of Reachability Sets in Vector Addition Systems with States

• Autorzy: Jančar Petr , Leroux Jérôme , Sutre Grégoire

Identyfikatory

DOI

10.3233/FI-2019-1841

• Języki publikacji: EN

Abstrakty

EN

The boundedness problem is a well-known exponential-space complete problem for vector addition systems with states (or Petri nets); it asks if the reachability set (for a given initial configuration) is finite. Here we consider a dual problem, the co-finiteness problem that asks if the complement of the reachability set is finite; by restricting the question we get the co-emptiness (or universality) problem that asks if all configurations are reachable. We show that both the co-finiteness problem and the co-emptiness problem are exponential-space complete. While the lower bounds are obtained by a straightforward reduction from coverability, getting the upper bounds is more involved; in particular we use the bounds derived for reversible reachability by Leroux (2013). The studied problems were motivated by a result for structural liveness of Petri nets; this problem was shown decidable by Jančar (2017), without clarifying its complexity. The structural liveness problem is tightly related to a generalization of the co-emptiness problem, where the sets of initial configurations are (possibly infinite) downward closed sets instead of just singletons. We formulate the problems even more generally, for semilinear sets of initial configurations; in this case we show that the co-emptiness problem is decidable (without giving an upper complexity bound), and we formulate a conjecture under which the co-finiteness problem is also decidable.

Słowa kluczowe

EN

vector addition system; Petri net; co-finite reachability set; universal reachability set; structural liveness; complexity

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2019
• Tom: Vol. 169, nr 1-2
• Strony: 123--150
• Opis fizyczny: Bibliogr. 20 poz., rys., tab.

Twórcy

autor

Jančar Petr

• Department of Computer Science, Faculty of Science, Palacký University, Olomouc, Czechia

autor

Leroux Jérôme

• Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, F-33400, Talence, France

autor

Sutre Grégoire

• Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, F-33400, Talence, France

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).