License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2023.36
URN: urn:nbn:de:0030-drops-190300
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/19030/
Jančar, Petr ;
Leroux, Jérôme
The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets
Abstract
A set of configurations H is a home-space for a set of configurations X of a Petri net if every configuration reachable from (any configuration in) X can reach (some configuration in) H. The semilinear home-space problem for Petri nets asks, given a Petri net and semilinear sets of configurations X, H, if H is a home-space for X. In 1989, David de Frutos Escrig and Colette Johnen proved that the problem is decidable when X is a singleton and H is a finite union of linear sets with the same periods. In this paper, we show that the general (semilinear) problem is decidable. This result is obtained by proving a duality between the reachability problem and the non-home-space problem. In particular, we prove that for any Petri net and any linear set of configurations L we can effectively compute a semilinear set C of configurations, called a non-reachability core for L, such that for every set X the set L is not a home-space for X if, and only if, C is reachable from X. We show that the established relation to the reachability problem yields the Ackermann-completeness of the (semilinear) home-space problem. For this we also show that, given a Petri net with an initial marking, the set of minimal reachable markings can be constructed in Ackermannian time.
BibTeX - Entry
@InProceedings{jancar_et_al:LIPIcs.CONCUR.2023.36,
author = {Jan\v{c}ar, Petr and Leroux, J\'{e}r\^{o}me},
title = {{The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets}},
booktitle = {34th International Conference on Concurrency Theory (CONCUR 2023)},
pages = {36:1--36:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-299-0},
ISSN = {1868-8969},
year = {2023},
volume = {279},
editor = {P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/19030},
URN = {urn:nbn:de:0030-drops-190300},
doi = {10.4230/LIPIcs.CONCUR.2023.36},
annote = {Keywords: Petri nets, home-space property, semilinear sets, Ackermannian complexity}
}
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Keywords: |
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Petri nets, home-space property, semilinear sets, Ackermannian complexity |
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Collection: |
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34th International Conference on Concurrency Theory (CONCUR 2023) |
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Issue Date: |
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2023 |
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Date of publication: |
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07.09.2023 |
