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Markings in Perpetual Free-Choice Nets Are Fully Characterized by Their Enabled Transitions

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10877))

Abstract

A marked Petri net is lucent if there are no two different reachable markings enabling the same set of transitions, i.e., states are fully characterized by the transitions they enable. This paper explores the class of marked Petri nets that are lucent and proves that perpetual marked free-choice nets are lucent. Perpetual free-choice nets are free-choice Petri nets that are live and bounded and have a home cluster, i.e., there is a cluster such that from any reachable state there is a reachable state marking the places of this cluster. A home cluster in a perpetual net serves as a “regeneration point” of the process, e.g., to start a new process instance (case, job, cycle, etc.). Many “well-behaved” process models fall into this class. For example, the class of short-circuited sound workflow nets is perpetual. Also, the class of processes satisfying the conditions of the \(\alpha \) algorithm for process discovery falls into this category. This paper shows that the states in a perpetual marked free-choice net are fully characterized by the transitions they enable, i.e., these process models are lucent. Having a one-to-one correspondence between the actions that can happen and the state of the process, is valuable in a variety of application domains. The full characterization of markings in terms of enabled transitions makes perpetual free-choice nets interesting for workflow analysis and process mining. In fact, we anticipate new verification, process discovery, and conformance checking techniques for the subclasses identified.

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Notes

  1. 1.

    \(\bigcup Q = \bigcup _{X \in Q} X\) for some set of sets Q.

References

  1. van der Aalst, W.M.P.: The application of Petri nets to workflow management. J. Circ. Syst. Comput. 8(1), 21–66 (1998)

    Article  Google Scholar 

  2. van der Aalst, W.M.P.: Workflow verification: finding control-flow errors using Petri-net-based techniques. In: van der Aalst, W.M.P., Desel, J., Oberweis, A. (eds.) Business Process Management. LNCS, vol. 1806, pp. 161–183. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45594-9_11

    Chapter  Google Scholar 

  3. van der Aalst, W.M.P.: Mediating between modeled and observed behavior: the quest for the “Right” process. In: IEEE International Conference on Research Challenges in Information Science (RCIS 2013), pp. 31–43. IEEE Computing Society (2013)

    Google Scholar 

  4. van der Aalst, W.M.P.: Process Mining: Data Science in Action. Springer, Berlin (2016)

    Book  Google Scholar 

  5. van der Aalst, W.M.P., Adriansyah, A., van Dongen, B.: Replaying history on process models for conformance checking and performance analysis. WIREs Data Mining Knowl. Discov. 2(2), 182–192 (2012)

    Article  Google Scholar 

  6. van der Aalst, W.M.P., van Hee, K.M., ter Hofstede, A.H.M., Sidorova, N., Verbeek, H.M.W., Voorhoeve, M., Wynn, M.T.: Soundness of workflow nets: classification, decidability, and analysis. Formal Aspects Comput. 23(3), 333–363 (2011)

    Article  MathSciNet  Google Scholar 

  7. van der Aalst, W.M.P., Rubin, V., Verbeek, H.M.W., van Dongen, B.F., Kindler, E., Günther, C.W.: Process mining: a two-step approach to balance between underfitting and overfitting. Softw. Syst. Model. 9(1), 87–111 (2010)

    Article  Google Scholar 

  8. van der Aalst, W.M.P., Stahl, C.: Modeling Business Processes: A Petri Net Oriented Approach. MIT Press, Cambridge (2011)

    MATH  Google Scholar 

  9. van der Aalst, W.M.P., Weijters, A.J.M.M., Maruster, L.: Workflow mining: discovering process models from event logs. IEEE Trans. Knowl. Data Eng. 16(9), 1128–1142 (2004)

    Article  Google Scholar 

  10. Best, E.: Structure theory of Petri nets: the free choice hiatus. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) ACPN 1986. LNCS, vol. 254, pp. 168–205. Springer, Heidelberg (1987). https://doi.org/10.1007/978-3-540-47919-2_8

    Chapter  Google Scholar 

  11. Best, E., Desel, J., Esparza, J.: Traps characterize home states in free-choice systems. Theor. Comput. Sci. 101, 161–176 (1992)

    Article  MathSciNet  Google Scholar 

  12. 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

    Chapter  MATH  Google Scholar 

  13. Desel, J., Esparza, J.: Free Choice Petri Nets. Cambridge Tracts in Theoretical Computer Science, vol. 40. Cambridge University Press, Cambridge (1995)

    Book  Google Scholar 

  14. Dumas, M., La Rosa, M., Mendling, J., Reijers, H.: Fundamentals of Business Process Management. Springer, Berlin (2013)

    Book  Google Scholar 

  15. Esparza, J.: Reachability in live and safe free-choice Petri nets is NP-Complete. Theor. Comput. Sci. 198(1–2), 211–224 (1998)

    Article  MathSciNet  Google Scholar 

  16. 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

    Chapter  Google Scholar 

  17. Gaujala, 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)

    Article  MathSciNet  Google Scholar 

  18. Genrich, H.J., Thiagarajan, P.S.: A theory of bipolar synchronization schemes. Theor. Comput. Sci. 30(3), 241–318 (1984)

    Article  MathSciNet  Google Scholar 

  19. Kiepuszewski, B., ter Hofstede, A.H.M., van der Aalst, W.M.P.: Fundamentals of control flow in workflows. Acta Informatica 39(3), 143–209 (2003)

    Article  MathSciNet  Google Scholar 

  20. Murata, T.: Petri nets: properties, analysis and applications. Proc. IEEE 77(4), 541–580 (1989)

    Article  Google Scholar 

  21. Reisig, W.: Petri Nets: Modeling Techniques, Analysis, Methods, Case Studies. Springer, Berlin (2013)

    MATH  Google Scholar 

  22. Reisig, W., Rozenberg, G. (eds.): Lectures on Petri Nets I: Basic Models. LNCS, vol. 1491. Springer, Berlin (1998). https://doi.org/10.1007/3-540-65306-6

    Book  MATH  Google Scholar 

  23. Reisig, W., Rozenberg, G. (eds.): Lectures on Petri Nets II: Applications. LNCS, vol. 1492. Springer, Berlin (1998). https://doi.org/10.1007/3-540-65307-4

    Book  MATH  Google Scholar 

  24. Russell, N., van der Aalst, W.M.P., ter Hofstede, A.: Workflow Patterns: The Definitive Guide. MIT Press, Cambridge (2016)

    Google Scholar 

  25. Thiagarajan, P.S., Voss, K.: A fresh look at free choice nets. Inf. Control 61(2), 85–113 (1984)

    Article  MathSciNet  Google Scholar 

  26. Wehler, J.: Simplified proof of the blocking theorem for free-choice Petri nets. J. Comput. Syst. Sci. 76(7), 532–537 (2010)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Process and Data Science (PADS), RWTH Aachen University, Aachen, Germany

    Wil M. P. van der Aalst

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  1. Wil M. P. van der Aalst
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Correspondence to Wil M. P. van der Aalst .

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Editors and Affiliations

  1. University of Newcastle, Newcastle upon Tyne, United Kingdom

    Victor Khomenko

  2. École Centrale de Nantes, Nantes Cedex 3, France

    Olivier H. Roux

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van der Aalst, W.M.P. (2018). Markings in Perpetual Free-Choice Nets Are Fully Characterized by Their Enabled Transitions. In: Khomenko, V., Roux, O. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2018. Lecture Notes in Computer Science(), vol 10877. Springer, Cham. https://doi.org/10.1007/978-3-319-91268-4_16

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  • DOI: https://doi.org/10.1007/978-3-319-91268-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91267-7

  • Online ISBN: 978-3-319-91268-4

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