Sufficient Criteria for Applicability and Non-Applicability of Rule Sequences

Abstract

In several rule-based applications using graph transformation as underlying modeling technique the following questions arise: How can one be sure that a specific sequence of rules is applicable (resp. not applicable) on a given graph? Of course, it is possible to use a trial and error strategy to find out the answer to these questions. In this paper however, we will formulate suitable sufficient criteria for applicability and other ones for non-applicability. These criteria can be checked in a static way i.e. without trying to apply the whole rule sequence explicitly. Moreover if a certain criterion is not satisfied, then this is an indication for reasons why rule sequences may or may not be applicable. Consequently it is easier to rephrase critical rule sequences.
The results are formulated within the framework of double pushout (DPO) graph transformations with negative application conditions (NACs).