Transformation of Attributed Structures with Cloning (Long Version)

TL;DR

This paper introduces a formal framework for graph transformations that include cloning and attribute modification, enabling complex structure manipulations previously difficult to formalize.

Contribution

It generalizes the sesqui-pushout approach to handle attributed structures with cloning, providing a flexible and natural specification method for complex graph operations.

Findings

Framework supports various graph types and attributes.

Allows specification of complex cloning and attribute-changing operations.

Demonstrates applicability through multiple examples.

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.