Abstract
There are different semantics for Petri nets. The behavior of a Petri net is either its set of enabled firing sequences, the reachability graph, a set of process nets, a valid partial language, its branching process, or any other known semantics taken from the literature. Every semantics has different advantages in different applications. Some focus on the set of reachable states and can model conflicts well. Other focus on the control flow of actions and can directly specify concurrency. Yet, every semantics has its drawbacks. State graphs explode in size when there is concurrency. Sequential and partial languages explode in size if there is conflict. Furthermore, all semantics use different concepts, definitions, graphical representations, and related algorithms. In this paper, we introduce token trails to define whether a labeled Petri net is in the language of another Petri net. Using labeled Petri nets as a specification language, we show how to faithfully model behavior including conflict and concurrency. Furthermore, we prove that token trail semantics faithfully covers all other semantics of Petri nets and, thus, serves as a kind of meta semantics.
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References
van der Aalst, W.M.P., van Dongen, B.F.: Discovering Petri Nets from Event Logs. In: Jensen, K., van der Aalst, W.M.P., Balbo, G., Koutny, M., Wolf, K. (eds.) Transactions on Petri Nets and Other Models of Concurrency VII. LNCS, vol. 7480, pp. 372–422. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38143-0_10
van der Aalst, W.M.P., Carmona, J.: Process Mining Handbook. Springer (2022). https://doi.org/10.1007/978-3-031-08848-3
Bergenthum, R., Lorenz, R.: Verification of Scenarios in Petri Nets Using Compact Tokenflows. In: Fundamenta Informaticae, vol. 137, no. 1, pp. 117–142. IOS Press (2015)
Bergenthum, R.: Firing Partial Orders in a Petri Net. In: Buchs, D., Carmona, J. (eds.) PETRI NETS 2021. LNCS, vol. 12734, pp. 399–419. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-76983-3_20
Bergenthum, R.: Petrinetze: Grundlagen der Formalen Prozessanalyse. In: Prozessmanagement und Process-Mining, De Gruyter Studium, pp. 125–152. De Gruyter (2021)
Bergenthum, R., Kovar, J.: A First Glimpse at Petri Net Regions. In: Proceedings of Application and Theory of Petri Nets 2022, CEUR Workshop Proceedings 3167, pp. 60–68 (2022)
Best, E., Devillers, R.: Sequential and Concurrent Behaviour in Petri Net Theory. In: Theoretical Computer Science 55, nr. 1, pp. 87–136. Elsevier (1987)
Cortadella, J., Kishinevsky, M., Kondratyev, A., Lavagno, L., Yakovlev, A.: Hardware and Petri Nets Application to Asynchronous Circuit Design. In: Nielsen, M., Simpson, D. (eds.) ICATPN 2000. LNCS, vol. 1825, pp. 1–15. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44988-4_1
Desel, J., Reisig, W.: Place/Transition Petri Nets. In: Reisig, W., Rozenberg, G. (eds.) ACPN 1996. LNCS, vol. 1491, pp. 122–173. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-65306-6_15
Desel, J., Juhás, G.: What is a Petri Net? In: Ehrig, H., Juhás, G., Padberg, J., Rozenberg, G. (eds.) Unifying Petri Nets, Advances in Petri Nets, LNCS 2128, pp. 1–25. Springer, Cham (2001). https://doi.org/10.1007/3-540-45541-8_1
van Dongen, B.F., de Medeiros, A.K.A., Verbeek, H.M.W., Weijters, A.J.M.M., van der Aalst, W.M.P.: The ProM Framework: A New Era in Process Mining Tool Support. In: Ciardo, G., Darondeau, P. (eds.) ICATPN 2005. LNCS, vol. 3536, pp. 444–454. Springer, Heidelberg (2005). https://doi.org/10.1007/11494744_25
Dumas, M., La Rosa, M., Mendling, J., Reijers, H.A.: Fundamentals of Business Process Management. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-33143-5
Goltz, U., Reisig, W.: Processes of Place/Transition-Nets. In: Diaz, J. (eds.) Automata Languages and Programming, vol. 154, pp. 264–277. Springer, Heidelberg (1983). https://doi.org/10.1007/BFb0036914
Grabowski, J.: On Partial Languages. In: Fundamenta Informaticae, vol. 4, no. 2, pp. 427–498. IOS Press (1981)
Janicki, R., Koutny, M.: Structure of Concurrency. In: Theoretical Computer Science 112, no. 1, pp. 5–52. Elsevier (1993)
Juhás, G., Lorenz, R., Desel, J.: Can I Execute My Scenario in Your Net? In: Ciardo, G., Darondeau, P. (eds.) Proceedings of Application and Theory of Petri Nets 2005, LNCS 3536, pp. 289–308. Springer, Heidelberg (2005). https://doi.org/10.1007/11494744_17
Kiehn, A.: On the Interrelation Between Synchronized and Non-Synchronized Behavior of Petri Nets. In: Elektronische Informationsverarbeitung und Kybernetik, vol. 24, no. 1–2, pp. 3–18 (1988)
Peterson, J.L.: Petri Net Theory and the Modeling of Systems. Prentice-Hall, Englewood Cliffs (1981)
Pratt, V.: Modelling Concurrency with Partial Orders. In: International Journal of Parallel Programming 15, pp. 33–71 (1986)
Reisig, W.: Understanding Petri Nets - Modeling Techniques, Analysis Methods, Case Studies. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-33278-4
Vogler, W. (ed.): Modular Construction and Partial Order Semantics of Petri Nets. LNCS, vol. 625. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55767-9
Winskel, G.: Event Structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) ACPN 1986. LNCS, vol. 255, pp. 325–392. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-17906-2_31
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Bergenthum, R., Folz-Weinstein, S., Kovář, J. (2023). Token Trail Semantics – Modeling Behavior of Petri Nets with Labeled Petri Nets. In: Gomes, L., Lorenz, R. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2023. Lecture Notes in Computer Science, vol 13929. Springer, Cham. https://doi.org/10.1007/978-3-031-33620-1_16
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