Resource Equivalences in Petri Nets

  • Irina A. Lomazova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10258)


Tokens in Petri net models may represent a control flow state, or resources produced/consumed by transition firings. From the resource perspective a part of a Petri net marking can be considered as a store needed for ensuring some future system behavior. The talk is devoted to the study of several types of resource equivalence in Petri nets. A resource is defined as a part (submultiset) of a Petri net marking and two resources are called equivalent iff replacing one of them by another in any reachable marking does not change the observable Petri net behavior. We investigate decidability of resource equivalences, present an algorithm for computing its finite approximation, and discuss applicability of resource equivalences to state space reduction and adaptive system processing.


Conditional Similarity Generalize Resource Minimal Pair Resource Similarity Resource Equivalence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I would like to thank Vladimir Bashkin for the many years of collaborative research, of which this paper presents just a part.


  1. 1.
    Autant, C., Schnoebelen, P.: Place bisimulations in Petri nets. In: Jensen, K. (ed.) ICATPN 1992. LNCS, vol. 616, pp. 45–61. Springer, Heidelberg (1992). doi: 10.1007/3-540-55676-1_3 CrossRefGoogle Scholar
  2. 2.
    Baldan, P., Bonchi, F., Gadducci, F.: Encoding asynchronous interactions using open Petri nets. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 99–114. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-04081-8_8 CrossRefGoogle Scholar
  3. 3.
    Bashkin, V.A., Lomazova, I.A.: Petri nets and resource bisimulation. Fundam. Inf. 55, 101–114 (2003). MathSciNetzbMATHGoogle Scholar
  4. 4.
    Bashkin, V.A., Lomazova, I.A.: Resource similarities in Petri net models of distributed systems. In: Malyshkin, V.E. (ed.) PaCT 2003. LNCS, vol. 2763, pp. 35–48. Springer, Heidelberg (2003). doi: 10.1007/978-3-540-45145-7_4 CrossRefGoogle Scholar
  5. 5.
    Bashkin, V.A., Lomazova, I.A.: Similarity of generalized resources in Petri nets. In: Malyshkin, V. (ed.) PaCT 2005. LNCS, vol. 3606, pp. 27–41. Springer, Heidelberg (2005). doi: 10.1007/11535294_3 CrossRefGoogle Scholar
  6. 6.
    Bashkin, V.A., Lomazova, I.A.: Decidability of \(k\)-soundness for workflow nets with an unbounded resource. In: Koutny, M., Haddad, S., Yakovlev, A. (eds.) Transactions on Petri Nets and Other Models of Concurrency IX. LNCS, vol. 8910, pp. 1–18. Springer, Heidelberg (2014). doi: 10.1007/978-3-662-45730-6_1 Google Scholar
  7. 7.
    Dong, X., Fu, Y., Varacca, D.: Place bisimulation and liveness for open Petri nets. In: Fränzle, M., Kapur, D., Zhan, N. (eds.) SETTA 2016. LNCS, vol. 9984, pp. 1–17. Springer, Cham (2016). doi: 10.1007/978-3-319-47677-3_1 CrossRefGoogle Scholar
  8. 8.
    Farwer, B.: A linear logic view of object Petri nets. Fundam. Inf. 37(3), 225–246 (1999). MathSciNetzbMATHGoogle Scholar
  9. 9.
    Farwer, B., Lomazova, I.: A systematic approach towards object-based Petri net formalisms. In: Bjørner, D., Broy, M., Zamulin, A.V. (eds.) PSI 2001. LNCS, vol. 2244, pp. 255–267. Springer, Heidelberg (2001). doi: 10.1007/3-540-45575-2_26 CrossRefGoogle Scholar
  10. 10.
    Finkel, A.: The ideal theory for WSTS. In: Larsen, K.G., Potapov, I., Srba, J. (eds.) RP 2016. LNCS, vol. 9899, pp. 1–22. Springer, Cham (2016). doi: 10.1007/978-3-319-45994-3_1 CrossRefGoogle Scholar
  11. 11.
    Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere!. Theoret. Comput. Sci. 256(1), 63–92 (2001). MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Girard, J.Y.: Linear logic. Theoret. Comput. Sci. 50(1), 1–101 (1987). MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Heckel, R.: Open Petri nets as semantic model for workflow integration. In: Ehrig, H., Reisig, W., Rozenberg, G., Weber, H. (eds.) Petri Net Technology for Communication-Based Systems. LNCS, vol. 2472, pp. 281–294. Springer, Heidelberg (2003). doi: 10.1007/978-3-540-40022-6_14 CrossRefGoogle Scholar
  14. 14.
    Higman, G.: Ordering by divisibility in abstract algebras. Proc. Lond. Math. Soc. s3–2(1), 326–336 (1952). MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Hirshfeld, Y.: Congruences in commutative semigroups. Technical report ECS-LFCS-94-291, Department of Computer Science, University of Edinburgh (1994)Google Scholar
  16. 16.
    Jančar, P.: Decidability questions for bisimilarity of Petri nets and some related problems. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds.) STACS 1994. LNCS, vol. 775, pp. 581–592. Springer, Heidelberg (1994). doi: 10.1007/3-540-57785-8_173 CrossRefGoogle Scholar
  17. 17.
    Karp, R.M., Miller, R.E.: Parallel program schemata. J. Comput. Syst. Sci. 3(2), 147–195 (1969). MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Lasota, S.: Decidability border for Petri nets with data: WQO dichotomy conjecture. In: Kordon, F., Moldt, D. (eds.) PETRI NETS 2016. LNCS, vol. 9698, pp. 20–36. Springer, Cham (2016). doi: 10.1007/978-3-319-39086-4_3 CrossRefGoogle Scholar
  19. 19.
    Lomazova, I.A.: Nested Petri nets - a formalism for specification and verification of multi-agent distributed systems. Fundam. Inf. 43(1), 195–214 (2000). MathSciNetzbMATHGoogle Scholar
  20. 20.
    Lomazova, I.A.: Nested Petri nets: multi-level and recursive systems. Fundam. Inf. 47(3–4), 283–293 (2001). MathSciNetzbMATHGoogle Scholar
  21. 21.
    Lomazova, I.A., Romanov, I.V.: Analyzing compatibility of services via resource conformance. Fundam. Inf. 128(1–2), 129–141 (2013). MathSciNetzbMATHGoogle Scholar
  22. 22.
    Lomazova, I.A., Schnoebelen, P.: Some decidability results for nested Petri Nets. In: Bjøner, D., Broy, M., Zamulin, A.V. (eds.) PSI 1999. LNCS, vol. 1755, pp. 208–220. Springer, Heidelberg (2000). doi: 10.1007/3-540-46562-6_18 CrossRefGoogle Scholar
  23. 23.
    Milner, R.: Communication and Concurrency. Prentice-Hall Inc., Upper Saddle River (1989)zbMATHGoogle Scholar
  24. 24.
    Rédei, L.: The Theory of Finitely Generated Commutative Semigroups. Oxford University Press, New York (1965)zbMATHGoogle Scholar
  25. 25.
    Rosa-Velardo, F., de Frutos-Escrig, D.: Decidability and complexity of Petri nets with unordered data. Theoret. Comput. Sci. 412(34), 4439–4451 (2011). MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Schnoebelen, P., Sidorova, N.: Bisimulation and the reduction of Petri Nets. In: Nielsen, M., Simpson, D. (eds.) ICATPN 2000. LNCS, vol. 1825, pp. 409–423. Springer, Heidelberg (2000). doi: 10.1007/3-540-44988-4_23 CrossRefGoogle Scholar
  27. 27.
    Sidorova, N., Stahl, C.: Soundness for resource-constrained workflow nets is decidable. IEEE Trans. Syst. Man Cybern.: Syst. 43(3), 724–729 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia

Personalised recommendations