Parallelism and concurrency in high-level replacement systems

Abstract

High-level replacement systems are formulated in an axiomatic algebraic framework based on categories pushouts. This approach generalizes the well-known algebraic approach to graph grammars and several other types of replacement systems, especially the replacement of algebraic specifications which was recently introduced for a rule-based approach to modular system design. in this paper basic notions like productions, derivations, parellel and sequential independence are introduced for high-level replacement syetms leading to Church-Rosser, Parallelism and concurrency Theorems previously shown in the literature for special cases only. In the general case of high-level replacement systems specific conditions, called HLR1- and HLR2-conditions, are formulated in order to obtain these results. Several examples of high-level replacement systems are discussed and classified w.r.t. HLR1- and HLR2-conditions showing which of the results are valid in each case.