Double-pushout hypergraph rewriting through free completions

Abstract

A relationship between double-pushout rewriting of total and partial hypergraphs is established by means of free completions. Given a double-pushout transformation rule P of total hypergraphs, a corresponding double-pushout transformation rule P' of partial subhypergraphs can be found a priori such that double-pushout derivations by the application of P are free completions of double-pushout derivations by the application of P'. It allows a more efficient double-pushout rewriting of total hypergraphs by rewriting suitable partial hypergraphs and freely completing the resulting partial hypergraphs. The main results in this paper are actually established in the more general setting of hierarchical unary algebras.