Transition Adjacency Relation Computation Based on Unfolding: Potentials and Challenges

  • Jisheng Pei
  • Lijie WenEmail author
  • Xiaojun Ye
  • Akhil Kumar
  • Zijing Lin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10033)


Transition Adjacency Relation (TAR) has provided a useful perspective for process model similarity measurement. Motivated by recent developments of other similarity metrics, this article puts TAR computation in the context of Petri net unfolding. Apart from being significantly faster than existing TAR computation algorithms, unfolding-based TAR computation also provides the potentials of enhancement through combination with other metrics that can be obtained from unfolding, especially the popular Behavior Profiles. We show that TAR computation can generally be reduced to coverability problem and solved using unfolding. However, there are also questions to be answered regarding how to further exploit unfolding information for optimal efficiency and handle silent transitions. In this article, we discuss what has been learned from our research, and also point out the open issues.


Business process model Transition Adjacency Relation Petri net Complete finite prefix Cut-off events 



This work was supported by the General Program of National Natural Science Foundation of China (No. 61472207) and Key Program of Research and Development of MOST (No. 2016YFB1001101).


  1. 1.
    Zha, H., et al.: A workflow net similarity measure based on transition adjacency relations. Comput. Ind. 61(5), 463–471 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Weidlich, M., Mendling, J., Weske, M.: Efficient consistency measurement based on behavioral profiles of process models. Softw. Eng. IEEE Trans. 37(3), 410–429 (2011)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Esparza, J., Romer, S., Vogler, W.: An improvement of McMillan’s unfolding algorithm. Formal Methods Syst. Des. 20(3), 285–310 (2002)CrossRefzbMATHGoogle Scholar
  4. 4.
    Rozinat, A., van der Aalst, W.M.P.: Conformance checking of processes based on monitoring real behavior. Inf. Syst. 33(1), 64–95 (2008)CrossRefGoogle Scholar
  5. 5.
    Aalst, W.M.P.: Inheritance of business processes: a journey visiting four notorious problems. In: Ehrig, H., Reisig, W., Rozenberg, G., Weber, H. (eds.) Petri Net Technology for Communication-Based Systems. LNCS, vol. 2472, pp. 383–408. Springer, Heidelberg (2003). doi: 10.1007/978-3-540-40022-6_19 CrossRefGoogle Scholar
  6. 6.
    Dumas, M., Garcia-Banuelos, L., Dijkman, R.M.: Similarity search of business process models. IEEE Data Eng. Bull. 32(3), 23–28 (2009)Google Scholar
  7. 7.
    Van Der Aalst, W.M.P.: Process Mining: Discovery, Conformance and Enhancement of Business Processes. Springer, Heidelberg (2011)CrossRefzbMATHGoogle Scholar
  8. 8.
    Prescher, J., Mendling, J., Weidlich, M.: The projected TAR and its application to conformance checking. In: Enterprise Modelling and Information Systems Architectures (EMISA) (2012)Google Scholar
  9. 9.
    Jin, T., Wang, J., Wen, L.: Efficient retrieval of similar workflow models based on behavior. In: Sheng, Q.Z., Wang, G., Jensen, C.S., Xu, G. (eds.) APWeb 2012. LNCS, vol. 7235, pp. 677–684. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-29253-8_64 CrossRefGoogle Scholar
  10. 10.
    Weidlich, M., Elliger, F., Weske, M.: Generalised computation of behavioural profiles based on petri-net unfoldings. In: Bravetti, M., Bultan, T. (eds.) WS-FM 2010. LNCS, vol. 6551, pp. 101–115. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-19589-1_7 CrossRefGoogle Scholar
  11. 11.
    Fahland, D., Favre, C., Jobstmann, B., Koehler, J., Lohmann, N., Völzer, H., Wolf, K.: Instantaneous soundness checking of industrial business process models. In: Dayal, U., Eder, J., Koehler, J., Reijers, H.A. (eds.) BPM 2009. LNCS, vol. 5701, pp. 278–293. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-03848-8_19 CrossRefGoogle Scholar
  12. 12.
    Pei, J., Wen, L., Ye, X.: Computation of Transition Adjacency Relations Based on complete finite prefix (Technical Report) arXiv preprint (2015). arXiv:1506.01428
  13. 13.
    Murata, T.: Petri nets: Properties, analysis and applications. Proc. IEEE 77(4), 541–580 (1989)CrossRefGoogle Scholar
  14. 14.
    Polyvyanyy, A., et al.: On the expressive power of behavioral profiles. Formal Aspects Comput. 28, 1–17 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Rodríguez, C., Schwoon, S.: Cunf: a tool for unfolding and verifying petri nets with read arcs. In: Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 492–495. Springer, Heidelberg (2013). doi: 10.1007/978-3-319-02444-8_42 CrossRefGoogle Scholar
  16. 16.
    Armas-Cervantes, A., Baldan, P., Dumas, M., García-Bañuelos, L.: Behavioral comparison of process models based on canonically reduced event structures. In: Sadiq, S., Soffer, P., Völzer, H. (eds.) BPM 2014. LNCS, vol. 8659, pp. 267–282. Springer, Heidelberg (2014). doi: 10.1007/978-3-319-10172-9_17 Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Jisheng Pei
    • 1
  • Lijie Wen
    • 1
    Email author
  • Xiaojun Ye
    • 1
  • Akhil Kumar
    • 2
  • Zijing Lin
    • 3
  1. 1.School of SoftwareTsinghua UniversityBeijingPeople’s Republic of China
  2. 2.Smeal College of BusinessPenn State UniversityState CollegeUSA
  3. 3.Division of Applied MathematicsBrown UniversityProvidenceUSA

Personalised recommendations