Parallel High - Level Replacement

High-level replacement systems are an axiomatic categorical framework based on double-pushouts in order to unify replacement systems like grammars for diierent kinds of graphs and relational structures or other types of structures like algebraic speciications. 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 diierent types of parallel replacement which are compared to each other in diierent parallel replacement theorems. An abstract version of a window-based graph editor and movement of objects in con-guration spaces are presented as examples of parallel high-level replacement systems.