Granularity of Conflicts and Dependencies in Graph Transformation Systems

Conflict and dependency analysis (CDA) is a static analysis for the detection of conflicting and dependent rule applications in a graph transformation system. The state-of-the-art CDA technique, critical pair analysis, provides its users the benefits of completeness, i.e., its output contains a precise representation of each potential conflict and dependency in a minimal context, called critical pair. Yet, user feedback has shown that critical pairs can be hard to understand; users are interested in core information about conflicts and dependencies occurring in various combinations. In this paper, we investigate the granularity of conflicts and dependencies in graph transformation systems. We introduce a variety of new concepts on different granularity levels: We start with conflict atoms, representing individual graph elements as smallest building bricks that may cause a conflict. We show that each conflict atom can be extended to at least one conflict reason and, conversely, each conflict reason is covered by atoms. Moreover, we relate conflict atoms to minimal conflict reasons, representing smallest element sets to be overlapped in order to obtain a pair of conflicting transformations. We show how conflict reasons are related to critical pairs. Finally, we introduce dual concepts for dependency analysis. As we discuss in a running example, our concepts pave the way for an improved CDA technique.