ALGEBRAIC TRANSFORMATION OF UNARY PARTIAL ALGEBRAS .1. DOUBLE-PUSHOUTAPPROACH

The transformation of total graph structures has been studied from the algebraic point of view for more than two decades now, and it has mot ivated the development of the so-called double-pushout and single-push out approaches to graph transformation. In this article we extend the double-pushout approach to the algebraic transformation of partial man y-sorted unary algebras. Such a generalization has been motivated by t he need to model the transformation of structures which are richer and more complex than acyclic graphs and hypergraphs. The main result pre sented in this article is an algebraic characterization of the double- pushout transformation in the categories of all homomorphisms and all closed homomorphisms of unary partial algebras over a given signature, together with a corresponding operational characterization which may serve as a basis for implementation. Moreover, both categories are sho wn to satisfy the strongest of the HLR (high level replacement) condit ions with respect to closed monomorphisms. HLR conditions are fundamen tal to rewriting because they guarantee the satisfaction of many rewri ting theorems concerning confluence, parallelism and concurrency.