In: Luca Aceto, Anna Ingólfsdóttir (Eds.): Lecture Notes in Computer Science, 3921: Foundations of Software Science and Computation Structures: 9th International Conference, FOSSACS 2006, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2006, Vienna, Austria, March 25-31, 2006, pages 202-216. Springer-Verlag, January 2006. URL: http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/1169063414,.
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.
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