Checking Graph-Transformation Systems for Confluence

Abstract

In general, it is undecidable whether a terminating graph-transformation system is confluent or not. We introduce the class of coverable hypergraph-transformation systems and show that confluence is decidable for coverable systems that are terminating. Intuitively, a system is coverable if its typing allows to extend each critical pair with a non-deletable context that uniquely identifies the persistent nodes of the pair. The class of coverable systems includes all hypergraph-transformation systems in which hyperedges can connect arbitrary sequences of nodes, and all graph-transformation systems with a sufficient number of unused edge labels.