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.2023.6
URN: urn:nbn:de:0030-drops-190005
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/19000/
Go to the corresponding LIPIcs Volume Portal

Guttenberg, Roland ; Raskin, Mikhail ; Esparza, Javier

Geometry of Reachability Sets of Vector Addition Systems

pdf-format:
LIPIcs-CONCUR-2023-6.pdf (0.8 MB)

Abstract

Vector Addition Systems (VAS), aka Petri nets, are a popular model of concurrency. The reachability set of a VAS is the set of configurations reachable from the initial configuration. Leroux has studied the geometric properties of VAS reachability sets, and used them to derive decision procedures for important analysis problems. In this paper we continue the geometric study of reachability sets. We show that every reachability set admits a finite decomposition into disjoint almost hybridlinear sets enjoying nice geometric properties. Further, we prove that the decomposition of the reachability set of a given VAS is effectively computable. As a corollary, we derive a new proof of Hauschildt’s 1990 result showing the decidability of the question whether the reachability set of a given VAS is semilinear. As a second corollary, we prove that the complement of a reachability set, if it is infinite, always contains an infinite linear set.

BibTeX - Entry

@InProceedings{guttenberg_et_al:LIPIcs.CONCUR.2023.6,
  author =	{Guttenberg, Roland and Raskin, Mikhail and Esparza, Javier},
  title =	{{Geometry of Reachability Sets of Vector Addition Systems}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{6:1--6:16},
  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/2023/19000},
  URN =		{urn:nbn:de:0030-drops-190005},
  doi =		{10.4230/LIPIcs.CONCUR.2023.6},
  annote =	{Keywords: Vector Addition System, Petri net, Reachability Set, Almost hybridlinear, Partition, Geometry}
}

Keywords: Vector Addition System, Petri net, Reachability Set, Almost hybridlinear, Partition, Geometry
Collection: 34th International Conference on Concurrency Theory (CONCUR 2023)
Issue Date: 2023
Date of publication: 07.09.2023

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI