Single-pushout hypergraph rewriting through free completions

Abstract

Different relationships between single-pushout rewriting of total and partial unary algebras are studied in this paper. In general, given a single-pushout transformation rule r of total algebras, a corresponding single-pushout transformation rule r' of partial algebras can be found such that single-pushout derivations by the application of r are epireflections of single-pushout derivations by the application of r' But, unlike the case of double-pushout derivations, in this case single-pushout transformation rules of partial algebras become "larger" than corresponding rules of total algebras. Therefore, ad hoc methods are developed to compute pushouts of partial homomorphisms through free completions which, in the case of hypergraphs, may lead to a slight improvement in efficiency of pattern-matching and to a moderate improvement in efficiency of single-pushout transformations.