Non-Deterministic Matching Algorithm for Net Transformations

Abstract

Modeling and simulating dynamic systems require to represent their processes and the system changes within one model. To that effect, reconfigurable Petri nets consist of a  place/transition net and a set of rules that can  modify the Petri net. The application of a rule is based on finding a suitable match of the rule in the given net. This match is an isomorphic  subnet that  has to be located meeting  requirements of the rule application as well as the simulation. In this paper a non-deterministic algorithm is presented for the matching in reconfigurable Petri nets. It is an extension of the VF2 algorithm for graph (sub-)isomorphisms. We show that this extension is correct and complete.   Non-determinism  ensures that during simulation different matches can be found for  each transformation step and is hence crucial for the simulation. But non-determinism has not been present in the VF2 algorithm. For the matching algorithm non-determinism is proven.