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.FSTTCS.2018.31
URN: urn:nbn:de:0030-drops-99305
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9930/
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Finkel, Alain ; Leroux, Jérôme ; Sutre, Grégoire

Reachability for Two-Counter Machines with One Test and One Reset

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Abstract

We prove that the reachability relation of two-counter machines with one zero-test and one reset is Presburger-definable and effectively computable. Our proof is based on the introduction of two classes of Presburger-definable relations effectively stable by transitive closure. This approach generalizes and simplifies the existing different proofs and it solves an open problem introduced by Finkel and Sutre in 2000.

BibTeX - Entry

@InProceedings{finkel_et_al:LIPIcs:2018:9930,
  author =	{Alain Finkel and J{\'e}r{\^o}me Leroux and Gr{\'e}goire Sutre},
  title =	{{Reachability for Two-Counter Machines with One Test and One Reset}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software  Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Sumit Ganguly and Paritosh Pandya},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9930},
  URN =		{urn:nbn:de:0030-drops-99305},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.31},
  annote =	{Keywords: Counter machine, Vector addition system, Reachability problem, Formal verification, Presburger arithmetic, Infinite-state system}
}

Keywords: Counter machine, Vector addition system, Reachability problem, Formal verification, Presburger arithmetic, Infinite-state system
Collection: 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)
Issue Date: 2018
Date of publication: 05.12.2018

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