Abstract
Canonical derivations, previously studied for string and graph grammars only, are generalized from graph grammars to high-level replacement systems, short HLR-systems. These systems were recently introduced to provide a common categorical framework for different types of replacement systems on complex objects, including graphs, hypergraphs, structures and algebraic specifications. It turns out that basic results concerning synthesis and analysis of parallel derivation sequences in HLR-systems, obtained in previous papers, can be extended to construct canonical parallel derivation sequences which are optimal w.r.t. leftmost parallelism. The main results show the existence and uniqueness of canonical derivations under weak assumptions for the underlying categories of HLR-systems. These results are specialized to graphs, hypergraphs, Petri nets, algebraic specifications and others by classifying the underlying categories with respect to the assumptions. This leads to interesting new results for most of the corresponding HLR-systems.KeywordsGraph GrammarParallel ProductionProof IdeaParallel DerivationAlgebraic SpecificationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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