Skeleton Abstraction for Universal Temporal Properties

Uniform coloured Petri nets can be abstracted to their skeleton, the place/transition net that simply turns the coloured tokens into black tokens. A coloured net and its skeleton are related by a net morphism. For the application of the skeleton as an abstraction method in the model checking process, we need to establish a simulation relation between the state spaces of the two nets. Then, universal temporal properties (properties of the $ACTL^*$ logic) are preserved. The abstraction relation induced by a net morphism is not necessarily a simulation relation, due to a subtle issue related to deadlocks. We discuss several situations where the abstraction relation induced by a net morphism is as well a simulation relation, thus preserving $ACTL^*$ properties. We further propose a partition refinement algorithm for folding a place/transition net into a coloured net. This way, skeleton abstraction becomes available for models given as place/transition nets. Experiments demonstrate the capabilities of the proposed technology. Using skeleton abstraction, we are capable of solving problems that have not been solved before in the Model Checking Contest.