Asynchronous Box Calculus

  • Authors:
  • Raymond Devillers;Hanna Klaudel;Maciej Koutny;Franck Pommereau

  • Affiliations:
  • Département d'informatique, Université Libre de Bruxelles, B-1050 Bruxelles, Belgium;LACL, Université Paris 12, 61, avenue du général de Gaulle, 94010 Créteil, France;Department of Computing Science, University of Newcastle upon Tyne, NE1 7RU, UK;LACL, Université Paris 12, 61, avenue du général de Gaulle, 94010 Créteil, France

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 2003

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Abstract

IThe starting point of this paper is an algebraic Petri net framework allowing one to express net compositions, such as iteration and parallel composition, as well as transition synchronisation and restriction. We enrich the original model by introducing new constructs supporting asynchronous interprocess communication. Such a communication is made possible thanks to special 'buffer' places where different transitions (processes) may deposit and remove tokens. We also provide an abstraction mechanism, which hides buffer places, effectively making them private to the processes communicating through them. We then provide an algebra of process expressions, whose constants and operators directly correspond to those used in the Petri net framework. Such a correspondence is used to associate nets to process expressions in a compositional way. That the resulting algebra of expressions is consistent with the net algebra is demonstrated by showing that an expression and the corresponding net generate isomorphic transition systems. This results in the Asynchronous Box Calculus (or ABC), which is a coherent dual model, based on Petri nets and process expressions, suitable for modelling and analysing distributed systems whose components can interact using both synchronous and asynchronous communication.