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DOI: 10.4230/LIPIcs.FSTTCS.2012.173

Scope-bounded Multistack Pushdown Systems: Fixed-Point, Sequentialization, and Tree-Width

Authors: Salvatore La Torre and Gennaro Parlato

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

Abstract

We present a novel fixed-point algorithm to solve reachability of multi-stack pushdown systems restricted to runs where matching push and pop transitions happen within a bounded number of context switches. The followed approach is compositional, in the sense that the runs of the system are summarized by bounded-size interfaces. Moreover, it is suitable for a direct implementation and can be exploited to prove two new results. We give a sequentialization for this class of systems, i.e., for each such multi-stack pushdown system we construct an equivalent single-stack pushdown system that faithfully simulates the behavior of each thread. We prove that the behavior graphs (multiply nested words) for these systems have bounded tree-width, and thus a number of decidability results can be derived from Courcelle's theorem.

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Salvatore La Torre and Gennaro Parlato. Scope-bounded Multistack Pushdown Systems: Fixed-Point, Sequentialization, and Tree-Width. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 173-184, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{latorre_et_al:LIPIcs.FSTTCS.2012.173,
  author =	{La Torre, Salvatore and Parlato, Gennaro},
  title =	{{Scope-bounded Multistack Pushdown Systems: Fixed-Point, Sequentialization, and Tree-Width}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{173--184},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.173},
  URN =		{urn:nbn:de:0030-drops-38563},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.173},
  annote =	{Keywords: Model-checking, multi-threaded programs, sequentialization, tree-width}
}

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Scope-bounded Multistack Pushdown Systems: Fixed-Point, Sequentialization, and Tree-Width

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