Initial Conflicts and Dependencies: Critical Pairs Revisited

Abstract

Considering a graph transformation system, a critical pair represents a pair of conflicting transformations in a minimal context. A conflict between two direct transformations of the same structure occurs if one of the transformations cannot be performed in the same way after the other one has taken place. Critical pairs allow for static conflict and dependency detection since there exists a critical pair for each conflict representing this conflict in a minimal context. Moreover it is sufficient to check each critical pair for strict confluence to conclude that the whole transformation system is locally confluent. Since these results were shown in the general categorical framework of M-adhesive systems, they can be instantiated for a variety of systems transforming e.g. (typed attributed) graphs, hypergraphs, and Petri nets.