Relational Graph Rewritings

This note presents a new formalization of graph rewritings which generalizes traditional graph rewritings. Relational notions of graphs and their rewritings are introduced and several properties about graph rewritings are discussed using relational calculus (theory of binary relations). Single pushout approaches to graph rewritings proposed by Raoult and Kennaway are compared with our rewritings of relational (labeled) graph. Moreover a more general su cient condition for two rewritings to commute and a theorem concerning critical pairs useful to demonstrate the con uency of graph rewriting systems are also given.