Structured coalgebras and minimal HD-automata for the π-calculus

  • Authors:

  • Ugo Montanari;Marco Pistore

  • Affiliations:

  • Computer Science Department, University of Pisa, Pisa, Italy;Department of Information and Comm. Technology, University of Trento, Povo, Trento, Italy

  • Venue:
  • Theoretical Computer Science - Mathematical foundations of computer science 2000
  • Year:
  • 2005

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Abstract

The coalgebraic framework developed for the classical process algebras, and in particular its advantages concerning minimal realizations, does not fully apply to the π-calculus, due to the constraints on the freshly generated names that appear in the bisimulation.In this paper we propose to model the transition system of the π-calculus as a coalgebra on a category of name permutation algebras and to define its abstract semantics as the final coalgebra of such a category. We show that permutations are sufficient to represent in an explicit way fresh name generation, thus allowing for the definition of minimal realizations.We also link the coalgebraic semantics with a slightly improved version of history dependent (HD) automata, a model developed for verification purposes, where states have local names and transitions are decorated with names and name relations. HD-automata associated with agents with a bounded number of threads in their derivatives are finite and can be actually minimized. We show that the bisimulation relation in the coalgebraic context corresponds to the minimal HD-antomaton.