Processes for adhesive rewriting systems

  • Authors:

  • Paolo Baldan;Andrea Corradini;Tobias Heindel;Barbara König;Paweł Sobociński

  • Affiliations:

  • Dipartimento di Informatica, Università Ca' Foscari di Venezia, Italy;Dipartimento di Informatica, Università di Pisa, Italy;Institut für Formale Methoden der Informatik, Universität Stuttgart, Germany;Institut für Formale Methoden der Informatik, Universität Stuttgart, Germany;Computer Laboratory, University of Cambridge, United Kingdom

  • Venue:
  • FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
  • Year:
  • 2006

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Abstract

Rewriting systems over adhesive categories have been recently introduced as a general framework which encompasses several rewriting-based computational formalisms, including various modelling frameworks for concurrent and distributed systems. Here we begin the development of a truly concurrent semantics for adhesive rewriting systems by defining the fundamental notion of process, well-known from Petri nets and graph grammars. The main result of the paper shows that processes capture the notion of true concurrency—there is a one-to-one correspondence between concurrent derivations, where the sequential order of independent steps is immaterial, and (isomorphism classes of) processes. We see this contribution as a step towards a general theory of true concurrency which specialises to the various concrete constructions found in the literature.