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URN: urn:nbn:de:0030-drops-33448
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Approximating Petri Net Reachability Along Context-free Traces

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Abstract

We investigate the problem asking whether the intersection of a context-free language (CFL) and a Petri net language (PNL) (with reachability as acceptance condition) is empty. Our contribution to solve this long-standing problem which relates, for instance, to the reachability analysis of recursive programs over unbounded data domain, is to identify a class of CFLs called the finite-index CFLs for which the problem is decidable. The k-index approximation of a CFL can be obtained by discarding all the words that cannot be derived within a budget k on the number of occurrences of non-terminals. A finite-index CFL is thus a CFL which coincides with its k-index approximation for some k. We decide whether the intersection of a finite-index CFL and a PNL is empty by reducing it to the reachability problem of Petri nets with weak inhibitor arcs, a class of systems with infinitely many states for which reachability is known to be decidable. Conversely, we show that the reachability problem for a Petri net with weak inhibitor arcs reduces to the emptiness problem of a finite-index CFL intersected with a PNL.

BibTeX - Entry

@InProceedings{atig_et_al:LIPIcs:2011:3344,
  author =	{Mohamed Faouzi Atig and Pierre Ganty},
  title =	{{Approximating Petri Net Reachability Along Context-free Traces}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)},
  pages =	{152--163},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-34-7},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{13},
  editor =	{Supratik Chakraborty and Amit Kumar},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3344},
  URN =		{urn:nbn:de:0030-drops-33448},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2011.152},
  annote =	{Keywords: Petri nets, Context-free Grammars, Reachability Problem}
}

Keywords: Petri nets, Context-free Grammars, Reachability Problem
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)
Issue date: 2011
Date of publication: 2011


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