A Basic Parallel Process as a Parallel Pushdown Automaton

  • Authors:

  • J. C. M. Baeten;P. J. L. Cuijpers;P. J. A. van Tilburg

  • Affiliations:

  • Division of Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Division of Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Division of Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

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

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Abstract

We investigate the set of basic parallel processes, recursively defined by action prefix, interleaving, 0 and 1. Different from literature, we use the constants 0 and 1 standing for unsuccessful and successful termination in order to stay closer to the analogies in automata theory. We prove that any basic parallel process is rooted branching bisimulation equivalent to a regular process communicating with a bag (also called a parallel pushdown automaton) and therefore we can regard the bag as the prototypical basic parallel process. This result is closely related to the fact that any context-free process is either rooted branching bisimulation equivalent or contrasimulation equivalent to a regular process communicating with a stack, a result that is the analogy in process theory of the language theory result that any context-free language is the language of a pushdown automaton.