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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References
Bønneland, F., Dyhr, J., Jensen, P.G., Johannsen, M., Srba, J.: Simplification of CTL formulae for efficient model checking of Petri Nets. In: Khomenko, V., Roux, O.H. (eds.) PETRI NETS 2018. LNCS, vol. 10877, pp. 143–163. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91268-4_8
Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Trans. Program. Lang. Syst. 8(2), 244–263 (1986)
Desel, J.: On abstractions of nets. In: Rozenberg, G. (ed.) ICATPN 1990. LNCS, vol. 524, pp. 78–92. Springer, Heidelberg (1991). https://doi.org/10.1007/BFb0019970
Findlow, G.: Obtaining deadlock-preserving skeletons for coloured nets. In: Jensen, K. (ed.) ICATPN 1992. LNCS, vol. 616, pp. 173–192. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55676-1_10
Grumberg, O., Long, D.E.: Model checking and modular verification. ACM Trans. Program. Lang. Syst. 16(3), 843–871 (1994)
Jensen, K., Kristensen, L.M.: Coloured Petri Nets. Modelling and Validation of Concurrent Systems. Springer, Heidelberg (2009). https://doi.org/10.1007/b95112
Katz, S., Grumberg, O., Geist, D.: “Have i written enough properties?” - a method of comparison between specification and implementation. In: Pierre, L., Kropf, T. (eds.) CHARME 1999. LNCS, vol. 1703, pp. 280–297. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48153-2_21
Kordon, F., et al.: Complete Results for the 2019 Edition of the Model Checking Contest (2019). http://mcc.lip6.fr/2019/results.php
Lilius, J.: On the Folding of Algebraic Nets. Helsinki University of Technology (1995)
Milner, R.: Communication and Concurrency. Prentice Hall International Series in Computer Science. Prentice Hall, New York (1989)
Padbergx, J., Gajewsky, M., Ermel, C.: Rule-based refinement of high-level nets preserving safety properties. In: Proceedings of the FASE, vol. 1382, pp. 221–238 (1998)
Pinna, G.M.: How much is worth to remember? A taxonomy based on Petri Nets unfoldings. In: Kristensen, L.M., Petrucci, L. (eds.) PETRI NETS 2011. LNCS, vol. 6709, pp. 109–128. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21834-7_7
Penczek, W., Szreter, M., Gerth, R., Kuiper, R.: Improving partial order reductions for universal branching time properties. Fundamenta Informaticae 43(14), 245–267 (2000)
Rust, C., Tacken, J., Böke, C.: Pr/T-Net based seamless design of embedded real-time systems. In: Colom, J.-M., Koutny, M. (eds.) ICATPN 2001. LNCS, vol. 2075, pp. 343–362. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45740-2_20
Sliva, V.P., Murataxx, T., Shatz, S.M.: Protocol specification design using an object-based Petri Net formalism. Int. J. Softw. Eng. Knowl. Eng. 09(01), 97–125 (1999)
Schwarick, M., Rohr, C., Liu, F., Assaf, G., Chodak, J., Heiner, M.: Efficient unfolding of coloured Petri Nets using interval decision diagrams. In: Janicki, R., Sidorova, N., Chatain, T. (eds.) PETRI NETS 2020. LNCS, vol. 12152, pp. 324–344. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-51831-8_16
Vautherin, J.: Parallel systems specifications with coloured Petri nets and algebraic specifications. In: Rozenberg, G. (ed.) APN 1986. LNCS, vol. 266, pp. 293–308. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-18086-9_31
Wolf, K.: Petri Net model checking with LoLA 2. In: Khomenko, V., Roux, O.H. (eds.) PETRI NETS 2018. LNCS, vol. 10877, pp. 351–362. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91268-4_18
Wolf, K.: Portfolio management in explicit model checking. In: Proceedings of the PNSE (CEUR Workshop Proceedings), vol. 2651, pp. 10–28 (2020)
Wimmel, H., Wolf, K.: Applying CEGAR to the Petri Net state equation. Log. Meth. Comput. Sci. 8(3) (2012). https://doi.org/10.2168/LMCS-8(3:27)2012
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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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