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DOI: 10.4230/LIPIcs.FSTTCS.2012.301

Extending the Rackoff technique to Affine nets

Authors: Rémi Bonnet, Alain Finkel, and M. Praveen

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Abstract

We study the possibility of extending the Rackoff technique to Affine nets, which are Petri nets extended with affine functions. The Rackoff technique has been used for establishing EXPSPACE upper bounds for the coverability and boundedness problems for Petri nets. We show that this technique can be extended to strongly increasing Affine nets, obtaining better upper bounds compared to known results. The possible copies between places of a strongly increasing Affine net make this extension non-trivial. One cannot expect similar results for the entire class of Affine nets since coverability is Ackermann-hard and boundedness is undecidable. Moreover, it can be proved that model checking a logic expressing generalized coverability properties is undecidable for strongly increasing Affine nets, while it is known to be EXPSPACE-complete for Petri nets.

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Rémi Bonnet, Alain Finkel, and M. Praveen. Extending the Rackoff technique to Affine nets. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 301-312, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{bonnet_et_al:LIPIcs.FSTTCS.2012.301,
  author =	{Bonnet, R\'{e}mi and Finkel, Alain and Praveen, M.},
  title =	{{Extending the Rackoff technique to Affine nets}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{301--312},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.301},
  URN =		{urn:nbn:de:0030-drops-38688},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.301},
  annote =	{Keywords: Complexity of VASS, Affine nets, Rackoff technique, model checking, coverability, boundedness}
}

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DOI: 10.4230/LIPIcs.FSTTCS.2010.192

Place-Boundedness for Vector Addition Systems with one zero-test

Authors: Rémi Bonnet, Alain Finkel, Jérôme Leroux, and Marc Zeitoun

Published in: LIPIcs, Volume 8, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)

Abstract

Reachability and boundedness problems have been shown decidable for Vector Addition Systems with one zero-test. Surprisingly, place-boundedness remained open. We provide here a variation of the Karp-Miller algorithm to compute a basis of the downward closure of the reachability set which allows to decide place-boundedness. This forward algorithm is able to pass the zero-tests thanks to a finer cover, hybrid between the reachability and cover sets, reclaiming accuracy on one component. We show that this filtered cover is still recursive, but that equality of two such filtered covers, even for usual Vector Addition Systems (with no zero-test), is undecidable.

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Rémi Bonnet, Alain Finkel, Jérôme Leroux, and Marc Zeitoun. Place-Boundedness for Vector Addition Systems with one zero-test. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 192-203, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{bonnet_et_al:LIPIcs.FSTTCS.2010.192,
  author =	{Bonnet, R\'{e}mi and Finkel, Alain and Leroux, J\'{e}r\^{o}me and Zeitoun, Marc},
  title =	{{Place-Boundedness for Vector Addition Systems with one zero-test}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)},
  pages =	{192--203},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-23-1},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{8},
  editor =	{Lodaya, Kamal and Mahajan, Meena},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.192},
  URN =		{urn:nbn:de:0030-drops-28638},
  doi =		{10.4230/LIPIcs.FSTTCS.2010.192},
  annote =	{Keywords: Place-boundedness, vector addition system with one zero-test, Karp-Miller algorithm}
}

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Documents authored by Bonnet, Rémi

Extending the Rackoff technique to Affine nets

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Place-Boundedness for Vector Addition Systems with one zero-test

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