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

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

Evolution of negative application conditions on second-order graph rewriting

Graph grammars are a suitable formalism to modeling computational systems. This formalism is based on rules and data-driven transformations capable of simulating real systems, rules have application conditions and post conditions that can change the system state. Moreover the use of graphs allows an intuitive visual interface essential for the modeler. It is well known that software systems are always evolving, evolutions may range from minor refactorings or bug fixes to major interface changes or new architectural design. The formalization of these evolution processes in graph grammars is done via higher-order principles, which allows programmed higher-level rules to induce modifications on lower-level rules, the system rules. In this work, we extend the current framework of higher-order transformations for graph grammars in order to allow the evolution of rules with negative application conditions. Besides this extension, we provide the first working implementation of the whole framework of higher-order graph grammars in the Verigraph tool enabling the practical usage of this techniques.Gramática de grafos é um formalismo para modelagem de sistemas computacionais. Este formalismo é baseado em regras e transformações de dados capazes de simular sistemas reais, regras tem pré e pós condições de aplicação que podem mudar o estado do sistema. Além disso, o uso de grafos permite uma interface visual intuitiva, que é essencial para o modelador. Se sabe que sistemas computacionais estão sempre evoluindo, essas evoluções podem varias de pequenas refatorações ou correções de problemas, até mudanças maiores em interfaces ou nova arquitetura. A formalização deste processo de evolução em gramáticas de grafos é feita com base em regras de segunda ordem, que possibilitam induzir modificações nas regras da gramática de primeira ordem. Neste trabalho, nós estendemos o framework atual de gramáticas de grafos de segunda ordem de forma a permitir evolução de regras com condições negativas de aplicação. Além desta extensão, nós provemos a primeira implementação do framework de gramáticas de grafos de segunda ordem na ferramenta Verigraph, possibilitando assim o uso na prática destas técnicas

On the Essence of Parallel Independence for the Double-Pushout and Sesqui-Pushout Approaches

International audienceParallel 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