A Theory of Name Boundedness

  • Reiner Hüchting
  • Rupak Majumdar
  • Roland Meyer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8052)


We develop a theory of name-bounded π-calculus processes, which have a bound on the number of restricted names that holds for all reachable processes. Name boundedness reflects resource constraints in practical reconfigurable systems, like available communication channels in networks and address space limitations in software.

Our focus is on the algorithmic analysis of name-bounded processes. First, we provide an extension of the Karp-Miller construction that terminates and computes the coverability set for any name-bounded process. Moreover, the Karp-Miller tree shows that name-bounded processes have a pumping bound as follows. When a restricted name is distributed to a number of sequential processes that exceeds this bound, the name may be distributed arbitrarily. Second, using the bound, we construct a Petri net bisimilar to the name-bounded process. The Petri net keeps a reference count for each restricted name, and recycles names that are no longer in use. The pumping property ensures that bounded zero tests are sufficient for recycling. With this construction, name-bounded processes inherit decidability properties of Petri nets. In particular, reachability is decidable for them. We complement our decidability results by a non-primitive recursive lower bound.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amadio, R., Meyssonnier, C.: On decidability of the control reachability problem in the asynchronous π-calculus. Nord. J. Comp. 9(1), 70–101 (2002)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Bansal, K., Koskinen, E., Wies, T., Zufferey, D.: Structural counter abstraction. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 62–77. Springer, Heidelberg (2013)Google Scholar
  3. 3.
    Busi, N., Gorrieri, R.: Distributed semantics for the π-calculus based on Petri nets with inhibitor arcs. J. Log. Alg. Prog. 78(1), 138–162 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Busi, N., Zavattaro, G.: Deciding reachability problems in Turing-complete fragments of Mobile Ambients. Math. Struct. Comp. Sci. 19(6), 1223–1263 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Dam, M.: Model checking mobile processes. Inf. Comp. 129(1), 35–51 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Devillers, R., Klaudel, H., Koutny, M.: A compositional Petri net translation of general π-calculus terms. For. Asp. Comp. 20(4-5), 429–450 (2008)zbMATHCrossRefGoogle Scholar
  7. 7.
    Finkel, A., Goubault-Larrecq, J.: The theory of WSTS: The case of complete WSTS. In: Haddad, S., Pomello, L. (eds.) PETRI NETS 2012. LNCS, vol. 7347, pp. 3–31. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    He, C.: The decidability of the reachability problem for CCS! In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 373–388. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Karp, R.M., Miller, R.E.: Parallel program schemata. J. Comput. Syst. Sci. 3(2), 147–195 (1969)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Lipton, R.J.: The reachability problem requires exponential space. Technical report, Yale University, Department of Computer Science (1976)Google Scholar
  11. 11.
    Mayr, E.W., Meyer, A.R.: The complexity of the finite containment problem for Petri nets. JACM 28(3), 561–576 (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Meyer, R.: On boundedness in depth in the π-calculus. In: IFIP TCS. IFIP, vol. 273, pp. 477–489. Springer, Heidelberg (2008)Google Scholar
  13. 13.
    Meyer, R.: A theory of structural stationarity in the π-calculus. Acta Inf. 46(2), 87–137 (2009)zbMATHCrossRefGoogle Scholar
  14. 14.
    Meyer, R., Gorrieri, R.: On the relationship between π-calculus and finite place/transition Petri nets. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 463–480. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  15. 15.
    Meyer, R., Khomenko, V., Hüchting, R.: A polynomial translation of π-calculus (FCP) to safe Petri nets. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 440–455. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  16. 16.
    Milner, R.: Communicating and Mobile Systems: the π-Calculus. CUP (1999)Google Scholar
  17. 17.
    Montanari, U., Pistore, M.: Checking bisimilarity for finitary π-calculus. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 42–56. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  18. 18.
    Rackoff, C.: The covering and boundedness problems for vector addition systems. Theor. Comp. Sci. 6(2), 223–231 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Sangiorgi, D., Walker, D.: The π-calculus: a Theory of Mobile Processes. CUP (2001)Google Scholar
  20. 20.
    Wies, T., Zufferey, D., Henzinger, T.A.: Forward analysis of depth-bounded processes. In: Ong, L. (ed.) FOSSACS 2010. LNCS, vol. 6014, pp. 94–108. Springer, Heidelberg (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Reiner Hüchting
    • 1
  • Rupak Majumdar
    • 2
  • Roland Meyer
    • 1
  1. 1.University of KaiserslauternGermany
  2. 2.MPI-SWSGermany

Personalised recommendations