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

Authors Salvatore La Torre, Gennaro Parlato

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Salvatore La Torre
Gennaro Parlato

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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)


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.
  • Model-checking
  • multi-threaded programs
  • sequentialization
  • tree-width


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