Basic Results for Two Types of High-Level Replacement Systems

Abstract

The general idea of high-level replacement systems is to generalize the concept of graph transformation systems and graph grammars from graphs to all kinds of structures which are of interest in Computer Science and Mathematics. Within the algebraic approach of graph transformation this is possible by replacing graphs, graph morphisms, and pushouts (gluing) of graphs by objects, morphisms, and pushouts in a suitable category. Of special interest are categories for all kinds of labelled and typed graphs, hypergraphs, algebraic specifications and Petri nets. In this paper, we review the basic results for high-level replacement systems in the algebraic double-pushout approach in the symmetric case, where both rule morphisms belong to a distinguished class M. Moreover we present for the first time the asymmetric type of high-level replacement systems, where only the left rule morphism K → L belongs to M.