Compositional Reachability in Petri Nets

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8762)


We introduce a divide-and-conquer algorithm for a modified version of the reachability/coverability problem in 1-bounded Petri nets that relies on the compositional algebra of nets with boundaries: we consider the algebraic decomposition of the net of interest as part of the input. We formally prove the correctness of the technique and contrast the performance of our implementation with state-of-the-art tools that exploit partial order reduction techniques on the global net.


Model Check State Graph Label Transition System Reachability Problem Core Algorithm 
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  1. 1.
    Bonchi, F., Pous, D.: Checking NFA Equivalence with Bisimulations up to Congruence. In: PoPL (2013)Google Scholar
  2. 2.
    Bruni, R., Melgratti, H., Montanari, U., Sobociński, P.: Connector algebras for C/E and P/T nets’ Interactions. Logical Methods in Computer Science 9(3) (2013)Google Scholar
  3. 3.
    Bruni, R., Melgratti, H., Montanari, U.: A connector algebra for P/T nets interactions. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 312–326. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Cheng, A., Esparza, J., Palsberg, J.: Complexity results for 1-safe nets. In: Shyamasundar, R.K. (ed.) FSTTCS 1993. LNCS, vol. 761, pp. 326–337. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  5. 5.
    Clarke, E.M., Long, D., McMillan, K.: Compositional model checking. In: LiCS 1989, pp. 352–362 (1989)Google Scholar
  6. 6.
    Corbett, J.C.: Evaluating Deadlock Detection Methods for Concurrent Software. IEEE Transactions on Software Engineering 22(3), 161–180 (1996)CrossRefGoogle Scholar
  7. 7.
    Esparza, J., Heljanko, K.: Implementing LTL model checking with net unfoldings. In: Dwyer, M.B. (ed.) SPIN 2001. LNCS, vol. 2057, pp. 37–56. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Esparza, J., Heljanko, K.: Unfoldings: a partial-order approach to model checking. Springer (2008)Google Scholar
  9. 9.
    Esparza, J., Römer, S., Vogler, W.: An improvement of McMillan’s unfolding algorithm. Form Method Syst Des 30(3), 285–310 (2002)CrossRefGoogle Scholar
  10. 10.
    Heljanko, K., Khomenko, V., Koutny, M.: Parallelisation of the Petri Net Unfolding Algorithm. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 371–385. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Katis, P., Sabadini, N., Walters, R.F.C.: Span(Graph): A categorical algebra of transition systems. In: Johnson, M. (ed.) AMAST 1997. LNCS, vol. 1349, pp. 307–321. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  12. 12.
    Khomenko, V., Kondratyev, A., Koutny, M., Vogler, W.: Merged Processes — A New Condensed Representation of Petri Net Behaviour. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 338–352. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Khomenko, V., Koutny, M., Vogler, W.: Canonical prefixes of Petri net unfoldings. Acta Inform. 40(2), 95–118 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Koutny, M., Khomenko, V.: Linear Programming Deadlock Checking Using Partial Order Dependencies. Technical report, Newcastle University (2000)Google Scholar
  15. 15.
    Mayr, R., Clemente, L.: Advanced Automata Minimization. In: POPL (2013)Google Scholar
  16. 16.
    McMillan, K.: A technique of a state space search based on unfolding. Form. Method Syst. Des. 6(1), 45–65 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Milner, R.: A Calculus of Communicating Systems. Prentice Hall (1989)Google Scholar
  18. 18.
    Nielsen, M., Plotkin, G., Winskel, G.: Petri Nets, Event Structures and Domains, Part I. Theoretical Computer Science 13(1), 85–108 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Rodríguez, C., Schwoon, S.: Cunf: A Tool for Unfolding and Verifying Petri Nets with Read Arcs. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 492–495. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  20. 20.
    Schmidt, K.: LoLA A Low Level Analyser. In: Nielsen, M., Simpson, D. (eds.) ICATPN 2000. LNCS, vol. 1825, pp. 465–474. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  21. 21.
    Sobociński, P.: Representations of petri net interactions. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 554–568. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  22. 22.
    Sobociński, P., Stephens, O.: Penrose: Putting Compositionality to Work for Petri Net Reachability. In: Heckel, R., Milius, S. (eds.) CALCO 2013. LNCS, vol. 8089, pp. 346–352. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  23. 23.
    Sobociński, P., Stephens, O.: Reachability via compositionality in Petri nets. arXiv:1303.1399v1 (2013)Google Scholar
  24. 24.
    Sobociński, P., Stephens, O.: A Programming Language for Spatial Distribution of Net Systems. In: Ciardo, G., Kindler, E. (eds.) PETRI NETS 2014. LNCS, vol. 8489, pp. 150–169. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  25. 25.
    Starke, P.: Reachability analysis of Petri nets using symmetries. Systems Analysis Modelling Simulation 5, 292–303 (1991)MathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.ECSUniversity of SouthamptonUK

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