Single pushout transformations of equationally defined graph structures with applications to actor systems

Abstract

This work has practically been motivated by an approach of modelling actor systems using algebraic graph grammars. It turned out that essential requirements on graph structures modelling computational states could nicely be expressed as conditional equations.These and other examples lead then to a general investigation of single pushout transformations within categories of equationally defined graph structures i.e., certain algebras satisfying a set of given equations, and partial morphisms. Fundamentally we characterize pushouts in these equationally defined categories as the corresponding pushouts in the supercategory of graph structures without equations if and only if the pushout object already satisfies the given equations. For labeled graph structures this characterization can be inherited from the unlabeled case, but only for a restricted class of equations. For a special kind of so-called local equations in particular, interesting graph transformation results carry over to the new setting. The use and the effects of such equations are illustrated and discussed for corresponding graph grammar modellings of a client/server problem considered as an actor system.KeywordsAlgebraic Graph TransformationsEquationally Defined Graph StructuresActor Systems