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Asynchronous Box Calculus

Lookup NU author(s): Professor Maciej KoutnyORCiD



The 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 a characterisation of the operational step sequence semantics of composite nets. These developments lead to 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 fully compositional way. Moreover, a structural characterisation of the Petri net semantics of composite nets guides the definition of a structured operational semantics of process expressions. 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.

Publication metadata

Author(s): Devillers R, Klaudel M, Koutny M, Pommereau F

Publication type: Report

Publication status: Published

Series Title: Department of Computing Science Technical Report Series

Year: 2002

Pages: 45

Print publication date: 01/12/2002

Source Publication Date: December 2002

Report Number: 759

Institution: Department of Computing Science, University of Newcastle upon Tyne

Place Published: Newcastle upon Tyne