On the essence and initiality of conflicts

Understanding conflicts between transformations and rules is an important topic in algebraic graph transformation. A conflict occurs when two transformations are not parallel independent, that is, when after applying one of them the other can no longer occur. We contribute to this research thread by proposing a new characterization of the root causes of conflicts, called “conflict essences”. By exploiting a recently proposed characterization of parallel independence we easily show that the conflict essence of two transformations is empty iff they are parallel independent. Furthermore we show that conflict essences are smaller than the “conflict reasons” previously proposed, and that they uniquely determine the so-called “initial conflicts”. All results hold in categories of Set-valued functors, which include the categories of graphs and typed graphs, and several of them hold in the more general adhesive categories

On the essence of parallel independence for the double-pushout and sesqui-pushout approaches

Parallel independence between transformation steps is a basic notion in the algebraic approaches to graph transformation, which is at the core of some static analysis techniques like Critical Pair Analysis. We propose a new categorical condition of parallel independence and show its equivalence with two other conditions proposed in the literature, for both left-linear and non-left-linear rules. Next we present some preliminary experimental results aimed at comparing the three conditions with respect to computational efficiency. To this aim, we implemented the three conditions, for left-linear rules only, in the Verigraph system, and used them to check parallel independence of pairs of overlapping redexes generated from some sample graph transformation systems over categories of typed graphs

Granularity of conflicts and dependencies in graph transformation systems: A two-dimensional approach

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 all potential conflicts and dependencies in minimal context as critical pairs, for each pair of rules. Yet, critical pairs can be hard to understand; users are mainly interested in core information about conflicts and dependencies occurring in various combinations. In this paper, we present an approach to conflicts and dependencies in graph transformation systems based on two dimensions of granularity. The first dimension refers to the overlap considered between the rules of a given rule pair; the second one refers to the represented amount of context information about transformations in which the conflicts occur. We introduce a variety of new conflict notions, in particular, conflict atoms, conflict reasons, and minimal conflict reasons, relate them to the existing conflict notions of critical pairs and initial conflicts, and position all of these notions within our granularity approach. Finally, we introduce dual concepts for dependency analysis. As we discuss in a running example, our approach paves the way for an improved CDA technique. (C) 2018 Elsevier Inc. All rights reserved