Bounded Communication Reachability Analysis of Process Rewrite Systems with Ordered Parallelism

  • Authors:
  • Mihaela Sighireanu;Tayssir Touili

  • Affiliations:
  • Liafa, CNRS and University Paris Diderot, France;Liafa, CNRS and University Paris Diderot, France

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2009

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Abstract

We define a new model called O-PRS that extends the Process Rewrite Systems formalism with a new associative operator, ''@?'', that allows to model parallel composition while keeping the order between parallel processes. Indeed, sometimes, it is important to remember the order between the parallel processes. The reachability problem of O-PRS being undecidable, we develop tree automata techniques allowing to build polynomial finite representations of (1) the exact reachable configurations in O-PRS modulo various equivalences that omit the associativity of ''@?'', and (2) underapproximations of the reachable configurations if the associativity of ''@?'' is considered. We show that these underapproximations are exact if the number of communications between ordered parallel processes is bounded. We implemented our algorithms in a tool that was used for the analysis of a concurrent lexer server.