Combining Parallel Graph Rewriting and Quotient Graphs

We define two graph transformations, one by parallelizing graph rewrite rules, the other by taking quotients of graphs. The former consists in the exhaustive application of local transformations defined by graph rewrite rules expressed in a set-theoretic framework. Compared with other approaches to parallel rewriting, we allow a substantial amount of overlapping only restricted by a condition called the effective deletion property. This transformation can be reduced by factoring out possibly many equivalent matchings by the automorphism groups of the rules. The second transformation is based on the use of equivalence relations over graph items and offers a new way of performing simultaneous merging operations. The relevance of combining the two transformations is illustrated on a running example.