Conflict Essences for Transformation Rules with Nested Application Conditions -- Long Version

TL;DR

This paper extends the concept of conflict essences in graph transformation rules to support nested application conditions, enabling more precise conflict analysis in complex rule interactions.

Contribution

It introduces symbolic conflict essences for rules with nested conditions, enhancing conflict detection accuracy in graph transformation systems.

Findings

Conflict essences can be embedded to determine parallel dependence.

Extended conflict analysis applies to adhesive HLR categories.

Supports arbitrary nested application conditions in conflict detection.

Abstract

Conflict and dependency analysis is an important static analysis tool that provides an overview of the potential interactions of (graph) transformation rules. This analysis is based on critical pairs and initial conflicts, which represent conflicting transformations in a minimal context. However, the crucial information about a conflicting transformation pair is contained in much smaller structures, called disabling/conflict essences in existing research. Recently, we introduced disabling essences for rules with application conditions which contain the information on how an application condition can be violated by another rule. In this paper, we extend the notion of disabling essences to support not only application conditions in Alternating Quantifier Normal Form, but also arbitrary nested conditions. We introduce (symbolic) conflict essences that are constructed from disabling essences and which capture the interaction between two rules. We show that a transformation pair is parallel dependent if and only if a symbolic conflict essence can be embedded into it and relate symbolic conflict essences to initial conflicts for transformation rules with application conditions. We present our results for adhesive HLR categories, which includes several types of graph-like structures.