License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2016.1
URN: urn:nbn:de:0030-drops-57024
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5702/
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Leroux, Jérôme ; Schmitz, Sylvain

Ideal Decompositions for Vector Addition Systems (Invited Talk)

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Abstract

Vector addition systems, or equivalently Petri nets, are one of the most popular formal models for the representation and the analysis of parallel processes. Many problems for vector addition systems are known to be decidable thanks to the theory of well-structured transition systems. Indeed, vector addition systems with configurations equipped with the classical point-wise ordering are well-structured transition systems. Based on this observation, problems like coverability or termination can be proven decidable.

However, the theory of well-structured transition systems does not explain the decidability of the reachability problem. In this presentation, we show that runs of vector addition systems can also be equipped with a well quasi-order. This observation provides a unified understanding of the data structures involved in solving many problems for vector addition systems, including the central reachability problem.

BibTeX - Entry

@InProceedings{leroux_et_al:LIPIcs:2016:5702,
  author =	{J{\'e}r{\^o}me Leroux and Sylvain Schmitz},
  title =	{{Ideal Decompositions for Vector Addition Systems (Invited Talk)}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{1:1--1:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5702},
  URN =		{urn:nbn:de:0030-drops-57024},
  doi =		{10.4230/LIPIcs.STACS.2016.1},
  annote =	{Keywords: Petri net, ideal, well-quasi-order, reachability, verification}
}

Keywords: Petri net, ideal, well-quasi-order, reachability, verification
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016

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