Parallel high-level replacement systems

Abstract

High-level replacement systems are an axiomatic categorical framework based on doublepushouts in order to unify replacement systems like grammars for different kinds of graphs and relational structures or other types of structures like algebraic specifications. Parallel high-level replacement systems are introduced to formalize parallel rewriting of these high-level structures. On one hand this concept generalizes and extends parallel graph grammars presented so far in the algebraic approach by allowing other structures than graphs, on the other hand the kinds of replacement introduced for high-level replacement systems are extended by different types of parallel replacement which are compared to each other in different parallel replacement theorems. An abstract version of a window-based graph editor and movement of objects in configuration spaces are presented as examples of parallel high-level replacement systems.