Relational Graph Rewritings

to appear in Theoretical Computer Science ARelational 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 sufficient condition for two rewritings to commute and a theorem concerning critical pairs useful to demonstrate the confluency of graph rewriting systems are also given.Graph Rewritings without Gluing Conditions: This note presents a new formalization of graph rewritings which generalizes Ehrig\u27s graph derivations and Raoult\u27s graph rewritings. The graph rewritings, based on a primitive pushout construction in the category of graphs and partial functions preserving graph structures, can be alivays applied without gluing colditions only if a graph has a matching to a given rewriting rule. A more general suffincient condition for two rewritings to commute is also proved. The simplicity of our discussion cornes from the usage of relational calculus (theory of binary relations)