Transformation of Attributed Structures with Cloning

Abstract

Abstract. Copying, or cloning, is a basic operation used in the specification of many applications in computer science. However, when dealing with complex structures, like graphs, cloning is not a straightforward operation since a copy of a single vertex may involve (implicitly) copying many edges. Therefore, most graph transformation approaches forbid the possibility of cloning. We tackle this problem by providing a framework for graph transformations with cloning. We use attributed graphs and allow rules to change attributes. These two features (cloning/changing attributes) together give rise to a powerful formal specification approach. In order to handle different kinds of graphs and attributes, we first define the notion of attributed structures in an abstract way. Then we generalise the sesqui-pushout approach of graph transformation in the proposed general framework and give appropriate conditions under which attributed structures can be transformed. Finally, we instantiate our general framework with different examples, showing that many structures can be handled and that the proposed framework allows one to specify complex operations in a natural way.

The Pullback-Pushout Approach to Algebraic Graph Transformation

“…For attributed structures we follow the same approach as in [7]. Given a category G called the category of structures, with pullbacks and pushouts, a category A called the category of attributes, and two functors S : G !…”

“…Set and T : A ! Set, the category of attributed structures AttG and the category of partially attributed structures PAttG are defined as in [7]. The issue is that there are not enough pushouts in the category PAttG.…”

“…An attributed structure b G = (G, A, ↵) is said attributed over A, an attributed morphism b g = (g, a) is said attributed over a, and when a = id A then b g can be said attributed over A. As in [7], we assume that all horizontal arrows in the rules preserve attributes, and we will see that this implies that all horizontal arrows in the rewrite steps also preserve attributes. This implies that there are objects A, A 0 and A 0 and arrows a : A !…”

“…After showing in which sense the new approach extends agree, we propose a formal notion of locality for pb-po rules and a su cient condition to ensure it. Next we consider the enrichment of the pb-po with attributes, following the ideas developed in [7] for the sqpo approach. A key feature of this approach is to allow attributes of items of the host graph to be changed through the application of a rule, a feature that is possible thanks to the use of partially attributed structures.…”

Parallel Graph Rewriting with Overlapping Rules

“…Below, we define the notion of homomorphisms of pregraphs and graphs. This notion assumes the existence of homomorphisms over attributes [7]. Definition 6 (Pregraph and Graph Homomorphism).…”