A Programming Language for Spatial Distribution of Net Systems

  • Paweł Sobociński
  • Owen Stephens
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8489)


Petri nets famously expose concurrency directly in their statespace. Building on the work on the compositional algebra of nets with boundaries, we show how an algebraic decomposition allows one to expose both concurrency and spatial distribution in the statespace.

Concretely, we introduce a high-level domain specific language (DSL), PNBml, for the construction of nets in terms of their components. We use PNBml to express several well-known parametric examples.


Modelling approaches system design using nets net-based semantical logical and algebraic calculi 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abdulla, P.A., Iyer, S.P., Nylén, A.: SAT-Solving the Coverability Problem for Petri Nets. Formal Methods in System Design 24(1), 25–43 (2004)CrossRefGoogle Scholar
  2. 2.
    Abramsky, S., Coecke, B.: A categorical semantics of quantum protocols. In: LiCS 2004. IEEE Press (2004)Google Scholar
  3. 3.
    Arnold, A.: Nivat’s processes and their synchronization. TCS 281(1-2), 31–26 (2002)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Baldan, P., Corradini, A., Ehrig, H., Heckel, R.: Compositional modelling of reactive systems using open nets. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 502–518. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Best, E., Devillers, R., Koutny, M.: Petri Net Algebra. Springer (2001)Google Scholar
  6. 6.
    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
  7. 7.
    Bruni, R., Melgratti, H.C., Montanari, U., Sobociński, P.: Connector algebras for C/E and P/T nets’ interactions. Log. Meth. Comput. Sci. 9(3:16), 1–65 (2013)Google Scholar
  8. 8.
    Christensen, S., Hansen, N.D.: Coloured Petri Nets Extended With Place Capacities, Test Arcs and Inhibitor Arcs. In: Ajmone Marsan, M. (ed.) ICATPN 1993. LNCS, vol. 691, pp. 186–205. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  9. 9.
    Corbett, J.C.: Evaluating Deadlock Detection Methods for Concurrent Software. IEEE Transactions on Software Engineering 22(3), 161–180 (1996)CrossRefGoogle Scholar
  10. 10.
    Hoare, C.A.R.: Communicating Sequential Processes. Prentice Hall (1985)Google Scholar
  11. 11.
    Junker, B.H., Schreiber, F.: Analysis of Biological Networks. Wiley (2008)Google Scholar
  12. 12.
    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
  13. 13.
    Kennedy, A.: Relational Parametricity and Units of Measure. In: POPL 1997, pp. 442–455. ACM (1997)Google Scholar
  14. 14.
    Kindler, E.: A compositional partial order semantics for petri net components. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 235–252. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  15. 15.
    Koch, I.: Petri nets - a mathematical formalism to analyze chemical reaction networks. Molecular Informatics 29(12), 838–843 (2010)CrossRefGoogle Scholar
  16. 16.
    Lafont, Y.: Towards an algebraic theory of boolean circuits. J. Pure. Appl. Alg. 184, 257–310 (2003)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Mazurkiewicz, A.: Compositional semantics of pure place/transition systems. In: Rozenberg, G. (ed.) APN 1988. LNCS, vol. 340, pp. 307–330. Springer, Heidelberg (1988)CrossRefGoogle Scholar
  18. 18.
    McMillan, K.: A technique of a state space search based on unfolding. Form. Method Syst. Des. 6(1), 45–65 (1995)CrossRefGoogle Scholar
  19. 19.
    Milner, R.: A Calculus of Communicating Systems. Prentice Hall (1989)Google Scholar
  20. 20.
    Petri, C.A.: Communication with automata. Technical report, Air Force Systems Command, Griffiss Air Force Base, New York (1966)Google Scholar
  21. 21.
    Rathke, J., Sobociński, P., Stephens, O.: Decomposing Petri nets. arXiv:1304.3121v1 (2013)Google Scholar
  22. 22.
    Reisig, W.: Simple composition of nets. In: Franceschinis, G., Wolf, K. (eds.) PETRI NETS 2009. LNCS, vol. 5606, pp. 23–42. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  23. 23.
    Rutten, J.: A tutorial on coinductive stream calculus and signal flow graphs. Theor. Comput. Sci. 343(3), 443–481 (2005)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Schmidt, K.: How to calculate symmetries of Petri nets. Acta. Inf. 36, 545–590 (2000)MathSciNetCrossRefGoogle Scholar
  25. 25.
    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
  26. 26.
    Sobociński, P., Stephens, O.: Penrose: Putting Compositionality to Work for Petri Net Reachability. In: Heckel, R. (ed.) CALCO 2013. LNCS, vol. 8089, pp. 346–352. Springer, Heidelberg (2013)Google Scholar
  27. 27.
    Sobociński, P., Stephens, O.: Reachability via compositionality in Petri nets. arXiv:1303.1399v1 (2013)Google Scholar
  28. 28.
    van der Aalst, W.: Process Mining: Discovery, Conformance and Enhancement of Business Processes. Springer (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Paweł Sobociński
    • 1
  • Owen Stephens
    • 1
  1. 1.ECSUniversity of SouthamptonUK

Personalised recommendations