Abstract
We use sequences of t-induced T-nets and p-induced P-nets to convert free-choice nets into T-nets and P-nets while preserving properties such as well-formedness, liveness, lucency, pc-safety, and perpetuality. The approach is general and can be applied to different properties. This allows for more systematic proofs that “peel off” non-trivial parts while retaining the essence of the problem (e.g., lifting properties from T-net and P-net to free-choice nets).
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Notes
- 1.
\(\bigcup Q = \bigcup _{X \in Q} X\) for some set of sets Q.
- 2.
The notions of T-reduction and P-reduction are unrelated to the “Desel rules” for free-choice nets without frozen tokens [8]. We allow for “bigger steps” and can reduce nets with frozen tokens (i.e., there may be an infinite firing sequence starting from a strictly smaller marking).
- 3.
Note that \(\bullet {t_r}=\{p \mid (p,t_r) \in F^i\}\) depends on the net considered (here \(N^i\)).
References
van der Aalst, W.M.P.: Process Mining: Data Science in Action. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49851-4
van der Aalst, W.M.P.: Markings in perpetual free-choice nets are fully characterized by their enabled transitions. In: Khomenko, V., Roux, O.H. (eds.) PETRI NETS 2018. LNCS, vol. 10877, pp. 315–336. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91268-4_16
van der Aalst, W.M.P.: Markings in Perpetual Free-Choice Nets Are Fully Characterized by Their Enabled Transitions. CoRR, abs/1801.04315 (2018)
van der Aalst, W.M.P.: Lucent process models and translucent event logs. Fundamenta Informaticae 169(1–2), 151–177 (2019)
van der Aalst, W.M.P.: Free-Choice Nets With Home Clusters Are Lucent (Aug 2020) (Under Review)
Berthelot, G.: Checking properties of nets using transformations. In: Rozenberg, G. (ed.) Advances in Petri Nets 1985. Lecture Notes in Computer Science, vol. 222, pp. 19–40. Springer, Berlin (1986). https://doi.org/10.1007/BFb0016204
Best, E., Wimmel, H.: Structure theory of petri nets. 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. 162–224. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38143-0_5
Desel, J.: Reduction and design of well-behaved concurrent systems. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 166–181. Springer, Heidelberg (1990). https://doi.org/10.1007/BFb0039059
Desel, J., Esparza, J.: Free Choice Petri Nets, vol. 40. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge (1995)
Dixit, P.M., Verbeek, H.M.W., Buijs, J.C.A.M., van der Aalst, W.M.P.: Interactive data-driven process model construction. In: Trujillo, J.C., et al. (eds.) ER 2018. LNCS, vol. 11157, pp. 251–265. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00847-5_19
Esparza, J., Silva, M.: Circuits, handles, bridges and nets. In: Rozenberg, G. (ed.) ICATPN 1989. LNCS, vol. 483, pp. 210–242. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-53863-1_27
Gaujal, B., Haar, S., Mairesse, J.: Blocking a transition in a free choice net and what it tells about its throughput. J. Comput. Syst. Sci. 66(3), 515–548 (2003)
Hack, M.H.T.: Analysis of Production Schemata by Petri Nets. Master’s thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts (1972)
Thiagarajan, P.S., Voss, K.: A fresh look at free choice nets. Inf. Control 61(2), 85–113 (1984)
Wehler, J.: Simplified proof of the blocking theorem for free-choice petri nets. J. Comput. Syst. Sci. 76(7), 532–537 (2010)
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van der Aalst, W.M.P. (2021). Reduction Using Induced Subnets to Systematically Prove Properties for Free-Choice Nets. 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_11
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