Synchronized composition of graph grammar productions

Abstract

In the framework of the double-pushout approach to graph grammars, we propose a new notion of parallel composition, called synchronized composition, of production applications. Our aim is to allow (pairs of) productions which are possibly not parallel independent, to be applied in parallel, provided that they are not mutually exclusive. The notion of synchronized composition we propose is not comparable to amalgamation [BFH87], since two productions which are amalgable are not necessarily synchronizable, and viceversa. Our different idea of which productions should be applicable in parallel comes from our view of graph grammars as a generalization of Petri nets. The definitions and constructions we use are a conservative extension of the ones used in the classical theory of parallelism in the algebraic approach to graph grammars. Moreover, they can be the basis for the development of a more general concept of canonical derivations, and also for a generalization of the recently developed partial order and event structure semantics for graph grammars.