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Transition Systems Reduction: Balancing Between Precision and Simplicity

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Transactions on Petri Nets and Other Models of Concurrency XII

Part of the book series: Lecture Notes in Computer Science ((TOPNOC,volume 10470))

Abstract

Transition systems are a powerful formalism, which is widely used for process model representation. A number of approaches were proposed in the process mining field to tackle the problem of constructing transition systems from event logs. Existing approaches discover transition systems that are either too large or too small. In this paper we propose an original approach to discover transition systems that perfectly fit event logs and whose size is adjustable depending on the user’s need. The proposed approach allows the ability to achieve a required balance between simple and precise models.

This work is supported by the Basic Research Program at the National Research University Higher School of Economics in 2017 and the study was funded by RFBR and Moscow city Government according to the research project No. 15-37-70008 “mol_a_mos”.

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Notes

  1. 1.

    Note, that \( s_0 \in S \), since event log L contains at least one trace by Definition 1.

  2. 2.

    To be precise, transition t is marked in the figure not only with activity b but also with its frequency b / 8.

  3. 3.

    Formally, for a trace \(\langle \rangle \), a state \( s_0 \) should be considered. Nevertheless, we explicitly distinguish the initial state \( s_0 \) and the rare-behavior state \( s_{0ws}\).

References

  1. http://www.win.tue.nl/bpi/doku.php?id=2015:challenge&redirect=1id=2015/challenge

  2. http://fluxicon.com/blog/2015/05/bpi-challenge-2015/

  3. van der Aalst, W.M.P., Rubin, V., Verbeek, H.M.W., Dongen, B.F., Kindler, E., Günther, C.W.: Process mining: a two-step approach to balance between underfitting and overfitting. Software Syst. Model. 9(1), 87–111 (2008). http://dx.doi.org/10.1007/s10270-008-0106-z

    Article  Google Scholar 

  4. van der Aalst, W.M.P.: Process Mining - Discovery, Conformance and Enhancement of Business Processes. Springer, Heidelberg (2011). doi:10.1007/978-3-642-19345-3

    MATH  Google Scholar 

  5. Angluin, D.: Inference of reversible languages. J. ACM 29(3), 741–765 (1982). http://doi.acm.org/10.1145/322326.322334

    Article  MathSciNet  MATH  Google Scholar 

  6. Badouel, E., Bernardinello, L., Darondeau, P.: Polynomial algorithms for the synthesis of bounded nets. In: Mosses, P.D., Nielsen, M., Schwartzbach, M.I. (eds.) CAAP 1995. LNCS, vol. 915, pp. 364–378. Springer, Heidelberg (1995). doi:10.1007/3-540-59293-8_207

    Google Scholar 

  7. Badouel, E., Bernardinello, L., Darondeau, P.: The synthesis problem for elementary net systems is NP-complete. Theoret. Comput. Sci. 186, 107–134 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  8. Badouel, E., Darondeau, P.: Theory of regions. In: Reisig, W., Rozenberg, G. (eds.) ACPN 1996. LNCS, vol. 1491, pp. 529–586. Springer, Heidelberg (1998). doi:10.1007/3-540-65306-6_22

    Chapter  Google Scholar 

  9. Bergenthum, R., Desel, J., Lorenz, R., Mauser, S.: Process mining based on regions of languages. In: Alonso, G., Dadam, P., Rosemann, M. (eds.) BPM 2007. LNCS, vol. 4714, pp. 375–383. Springer, Heidelberg (2007). doi:10.1007/978-3-540-75183-0_27

    Chapter  Google Scholar 

  10. Biermann, A.W., Feldman, J.A.: On the synthesis of finite-state machines from samples of their behavior. IEEE Trans. Comput. 21(6), 592–597 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  11. Buijs, J.C.A.M., Dongen, B.F., van der Aalst, W.M.P.: On the role of fitness, precision, generalization and simplicity in process discovery. In: Meersman, R., Panetto, H., Dillon, T., Rinderle-Ma, S., Dadam, P., Zhou, X., Pearson, S., Ferscha, A., Bergamaschi, S., Cruz, I.F. (eds.) OTM 2012. LNCS, vol. 7565, pp. 305–322. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33606-5_19

    Chapter  Google Scholar 

  12. Carmona, J., Cortadella, J., Kishinevsky, M.: A region-based algorithm for discovering petri nets from event logs. In: Dumas, M., Reichert, M., Shan, M.-C. (eds.) BPM 2008. LNCS, vol. 5240, pp. 358–373. Springer, Heidelberg (2008). doi:10.1007/978-3-540-85758-7_26

    Chapter  Google Scholar 

  13. Cook, J.E., Wolf, A.L.: Discovering models of software processes from event-based data. ACM Trans. Softw. Eng. Methodol. 7(3), 215–249 (1998). http://doi.acm.org/10.1145/287000.287001

    Article  Google Scholar 

  14. Cortadella, J., Kishinevsky, M., Lavagno, L., Yakovlev, A.: Deriving petri nets from finite transition systems. IEEE Trans. Comput. 47(8), 859–882 (1998). http://dx.doi.org/10.1109/12.707587

    Article  MathSciNet  Google Scholar 

  15. Lorenzoli, D., Mariani, L., Pezzè, M.: Inferring state-based behavior models. In: 4th International Workshop on Dynamic Analysis (WODA 2006) co-located with the 28th International Conference on Software Engineering (ICSE 2006), pp. 25–32. ACM Press (2006)

    Google Scholar 

  16. Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981). doi:10.1007/BFb0017309

    Chapter  Google Scholar 

  17. Solé, M., Carmona, J.: Process mining from a basis of state regions. In: Lilius, J., Penczek, W. (eds.) PETRI NETS 2010. LNCS, vol. 6128, pp. 226–245. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13675-7_14

    Chapter  Google Scholar 

  18. Sole, M., Carmona, J.: Region-based foldings in process discovery. IEEE Trans. Knowl. Data Eng. 25(1), 192–205 (2013)

    Article  Google Scholar 

  19. Verbeek, H., Buijs, J., Dongen, B., Aalst, W.: ProM 6: the process mining toolkit. In: Rosa, M.L. (ed.) Proceeding of BPM Demonstration Track 2010, CEUR Workshop Proceedings, vol. 615, pp. 34–39 (2010)

    Google Scholar 

  20. van der Werf, J.M.E.M., van Dongen, B.F., Hurkens, C.A.J., Serebrenik, A.: Process discovery using integer linear programming. In: van Hee, K.M., Valk, R. (eds.) PETRI NETS 2008. LNCS, vol. 5062, pp. 368–387. Springer, Heidelberg (2008). doi:10.1007/978-3-540-68746-7_24

    Chapter  Google Scholar 

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Authors and Affiliations

  1. National Research University Higher School of Economics, 20 Myasnitskaya Street, 101000, Moscow, Russia

    Sergey A. Shershakov, Anna A. Kalenkova & Irina A. Lomazova

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  1. Sergey A. Shershakov
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  2. Anna A. Kalenkova
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  3. Irina A. Lomazova
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Correspondence to Sergey A. Shershakov .

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Editors and Affiliations

  1. Newcastle University, Newcastle upon Tyne, United Kingdom

    Maciej Koutny

  2. LIACS, Leiden University, Leiden, The Netherlands

    Jetty Kleijn

  3. Polish Academy of Sciences, Institute of Computer Science, Warsaw, Poland

    Wojciech Penczek

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Shershakov, S.A., Kalenkova, A.A., Lomazova, I.A. (2017). Transition Systems Reduction: Balancing Between Precision and Simplicity. In: Koutny, M., Kleijn, J., Penczek, W. (eds) Transactions on Petri Nets and Other Models of Concurrency XII. Lecture Notes in Computer Science(), vol 10470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55862-1_6

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  • DOI: https://doi.org/10.1007/978-3-662-55862-1_6

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