Algebraic transformation of unary partial algebras II: Single-pushout approach

AbstractThe single-pushout approach to graph transformation is extended to the algebraic transformation of partial many-sorted unary algebras. Such a generalization has been motivated by the need to model the transformation of structures which are richer and more complex than graphs and hypergraphs.The main result presented in this article is an algebraic characterization of the single-pushout transformation in the categories of all conformisms, all closed quomorphisms, and all closed-domain closed quomorphisms of unary partial algebras over a given signature, together with a corresponding operational characterization that may serve as a basis for implementation.Moreover, all three categories are shown to satisfy all of the HLR (high-level replacement) conditions for parallelism, taking as occurrences the total morphisms in each category. Another important result presented in this article is the definition of HLR conditions for amalgamation, which are also satisfied by the categories of partial homomorphisms considered here, taking again the corresponding total morphisms as occurrences

Hypergraph Rewriting Using Conformisms

In this paper we study single-pushout transformation in a category of spans, a generalization of the notion of partial morphism in, for instance, [2,4]. As an application, single-pushout transformation in a category of hypergraphs with a special type of partial morphisms, the conformisms, is presented. In particular, we show the existence of the pushout of any pair of conformisms of hypergraphs with the same source hypergraph, and how to construct one such a pushout. Finally, hypergraph rewriting using conformisms is compared to single-pushout hypergraph rewriting by means of a detailed example. We present in this paper an approach to hypergraph rewriting by means of single-pushout transformation in a category of hypergraphs with a special type of partial morphisms, the conformisms, inspired by the homonymous notion in the theory of partial algebras. Although this approach has already been treated by some of us in [1] by means of what we could call "rudeforce methods," in this paper we..