Adding Recursion to Graph Transformation

Abstract

In this paper we define recursive rules in the double pushout approach (DPO) to graph transformation. Classical DPO rules are extended with a base case condition and a recursion condition. Mechanisms are provided to pass the match from both conditions to the rule's left hand side, and also between two consecutive steps in the recursion. The approach is useful when recursive structures (such as inheritance hierarchies, nested component hierarchies, networks of functional blocks, etc.) have to be processed. Although we present the recursion for DPO, it can also be adapted to other approaches to graph and model transformation. We present examples for model transformation, model simulation and model optimization in different application domains.