Abstract True Concurrency: Adhesive Processes

True Concurrency: Adhesive Processes Paolo Baldan, Andrea Corradini, Tobias Heindel, Barbara König, and Pawe l Sobociński 1 Dipartimento di Informatica, Università Ca’ Foscari di Venezia, Italy 2 Dipartimento di Informatica, Università di Pisa, Italy 3 Institut für Formale Methoden der Informatik, Universität Stuttgart, Germany 4 Computer Laboratory, University of Cambridge, United Kingdom 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-toone correspondence between concurrent derivations, where the sequential order of independent steps is immaterial, and (isomorphism classes of) processes. We see this contribution as an important step towards a general theory of true concurrency which specialises to the various concrete constructions found in the literature. 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-toone correspondence between concurrent derivations, where the sequential order of independent steps is immaterial, and (isomorphism classes of) processes. We see this contribution as an important step towards a general theory of true concurrency which specialises to the various concrete constructions found in the literature.