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Theoretical Computer Science
Volume 211, Issues 1-2, 28 January 1999, Pages 1-83
 
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doi:10.1016/S0304-3975(97)00180-1    How to Cite or Link Using DOI (Opens New Window)
Copyright © 1999 Published by Elsevier Science B.V.

Fundamental study

Operational and denotational semantics for the box algebra

Maciej Koutnya, Corresponding Author Contact Information, E-mail The Corresponding Author and Eike Bestb, **

a Department of Computing Science, University of Newcastle, Newcastle upon Tyne NE1 7RU, UK b Institut für Informatik, Universität Hildesheim, Marienburger Platz 22, D-31141, Hildesheim, Germany

Communicated by G. Rozenberg 
Available online 3 March 1999.

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Abstract

This paper describes general theory underpinning the operational semantics and the denotational Petri net semantics of the box algebra including recursion. For the operational semantics, inductive rules for process expressions are given. For the net semantics, a general mechanism of refinement and relabelling is introduced, using which the connectives of the algebra are defined. The paper also describes a denotational approach to the Petri net semantics of recursive expressions. A domain of nets is identified such that the solution of a given recursive equation can be found by fixpoint approximation from some suitable starting point. The consistency of the two semantics is demonstrated. The theory is generic for a wide class of algebraic operators and synchronisation schemes.

Author Keywords: Petri nets; Process algebra; Refinement; Denotational semantics; Operational semantics; Recursion; Bisimulation

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