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Skeleton Abstraction for Universal Temporal Properties

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12734)

Abstract

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 [Des91, PGE98]. For the application of the skeleton as an abstraction method in the model checking process, we need to establish a simulation relation [Mil89] 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 [Fin92]. 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 [KGH+19].

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Wallner, S., Wolf, K. (2021). Skeleton Abstraction for Universal Temporal Properties. In: Buchs, D., Carmona, J. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2021. Lecture Notes in Computer Science(), vol 12734. Springer, Cham. https://doi.org/10.1007/978-3-030-76983-3_10

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  • DOI: https://doi.org/10.1007/978-3-030-76983-3_10

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