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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73597332" target="_blank" >RIV/61989592:15310/19:73597332 - isvavai.cz</a>

Result on the web

<a href="https://content.iospress.com/articles/fundamenta-informaticae/fi1841" target="_blank" >https://content.iospress.com/articles/fundamenta-informaticae/fi1841</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3233/FI-2019-1841" target="_blank" >10.3233/FI-2019-1841</a>

Result language

angličtina

Original language name

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

Original language description

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 Jancar (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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GA18-11193S" target="_blank" >GA18-11193S: Algorithms for Infinite-State Discrete Systems and Games</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

FUNDAMENTA INFORMATICAE

ISSN

0169-2968

e-ISSN

—

Volume of the periodical

169

Issue of the periodical within the volume

1-2

Country of publishing house

PL - POLAND

Number of pages

28

Pages from-to

123-150

UT code for WoS article

000489900300006

EID of the result in the Scopus database

2-s2.0-85073729714