Applying the Graph Minor Theorem to the Verification of Graph Transformation Systems

Abstract

We show how to view certain subclasses of (single-pushout) graph transformation systems as well-structured transition systems, which leads to decidability of the covering problem via a backward analysis. As the well-quasi order required for a well-structured transition system we use the graph minor ordering. We give an explicit construction of the backward step and apply our theory in order to show the correctness of a leader election protocol.