Acta Informatica

, Volume 46, Issue 2, pp 87–137 | Cite as

A theory of structural stationarity in the π-Calculus

  • Roland Meyer
Original Article


Automata-theoretic representations have proven useful in the automatic and exact analysis of computing systems. We propose a new semantical mapping of π-Calculus processes into place/transition Petri nets. Our translation exploits the connections created by restricted names and can yield finite nets even for processes with unbounded name and unbounded process creation. The property of structural stationarity characterises the processes mapped to finite nets. We provide exact conditions for structural stationarity using novel characteristic functions. As application of the theory, we identify a rich syntactic class of structurally stationary processes, called finite handler processes. Our Petri net translation facilitates the automatic verification of a case study modelled in this class.


Sequential Process Parallel Composition Structural Semantic Restricted Form Free Agent 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amadio R.M., Meyssonnier C.: On decidability of the control reachability problem in the asynchronous π-calculus. Nord. J. Comput. 9(1), 70–101 (2002)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Bodei, C., Degano, P., Nielson, F., Riis Nielson, H.: Control flow analysis for the π-calculus. In: Proc. of the 9th International Conference on Concurrency Theory, CONCUR. LNCS, vol. 1466, pp. 84–98. Springer, Heidelberg (1998)Google Scholar
  3. 3.
    Busi, N., Gorrieri, R.: A Petri net semantics for π-calculus. In: Proc. of the 6th International Conference on Concurrency Theory, CONCUR. LNCS, vol. 962, pp. 145–159. Springer, Heidelberg (1995)Google Scholar
  4. 4.
    Busi, N., Gorrieri, R.: Distributed semantics for the π-calculus based on Petri nets with inhibitor arcs. Journal of Logic and Algebraic Programming, 46 pp. (2008, to appear)Google Scholar
  5. 5.
    Busi N.: Analysis issues in Petri nets with inhibitor arcs. Theor. Comput. Sci. 275(1–2), 127–177 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Caires, L.: Behavioural and spatial observations in a logic for the π-Calculus. In: Proc. of the 7th International Conference on Foundations of Software Science and Computation Structures, FOSSACS. LNCS, vol. 2987, pp. 72–89. Springer, Heidelberg (2004) Spatial Logic Model Checker:
  7. 7.
    Caires L., Cardelli L.: A spatial logic for concurrency (part I). Inf. Comput. 186(2), 194–235 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Clarke, E. M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Proc. of the 12th International Conference on Computer Aided Verification, CAV. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000)Google Scholar
  9. 9.
    Clarke E. M., Grumberg O., Peled D.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  10. 10.
    Dam M.: Model checking mobile processes. Inf. Comput. 129(1), 35–51 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Devillers R., Klaudel H., Koutny M.: A Petri net semantics of the finite π-Calculus terms. Fundam. Inf. 70(3), 203–226 (2006)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Devillers, R., Klaudel, H., Koutny, M.: A Petri net translation of π-Calculus terms. In: Proc. of the 3rd International Colloquium on Theoretical Aspects of Computing, ICTAC. LNCS, vol. 4281, pp. 138–152. Springer, Heidelberg (2006)Google Scholar
  13. 13.
    Engelfriet J., Gelsema T.: Multisets and structural congruence of the pi-calculus with replication. Theor. Comput. Sci. 211(1-2), 311–337 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Engelfriet, J., Gelsema, T.: The decidability of structural congruence for replication restricted pi-calculus processes. Technical report, Leiden Institute of Advanced Computer Science (2004). Revised 2005Google Scholar
  15. 15.
    Engelfriet J., Gelsema T.: A new natural structural congruence in the pi-calculus with replication. Acta Inf. 40(6), 385–430 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Engelfriet J., Gelsema T.: An exercise in structural congruence. Inf. Process. Lett. 101(1), 1–5 (2007)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Engelfriet J.: A multiset semantics for the pi-calculus with replication. Theor. Comput. Sci. 153(1–2), 65–94 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Esparza J., Römer S., Vogler W.: An improvement of McMillan’s unfolding algorithm. Formal Methods Syst. Des. 20(3), 285–310 (2002)zbMATHCrossRefGoogle Scholar
  19. 19.
    Esparza, J., Schröter, C.: Net reductions for LTL model-checking. In: Proc. of the 11th Advanced Research Working Conference on Correct Hardware Design and Verification Methods, CHARME. LNCS, vol. 2144, pp. 310–324. Springer, Heidelberg (2001)Google Scholar
  20. 20.
    Esparza J.: Decidability of model checking for infinite-state concurrent systems. Acta Inf. 34(2), 85–107 (1997)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Esparza J.: Petri Nets, commutative context-free grammars, and basic parallel processes. Fundam. Inf. 31(1), 13–25 (1997)zbMATHMathSciNetGoogle Scholar
  22. 22.
    Ferrari, G.-L., Gnesi, S., Montanari, U., Pistore, M.: A model-checking verification environment for mobile processes. ACM Trans. Softw. Eng. Methodol. 12(4):440–473 (2003). HAL: Google Scholar
  23. 23.
    Hsu, A., Eskafi, F., Sachs, S., Varaiya, P.: Design of platoon maneuver protocols for ivhs. Path research report, Institute of Transportation Studies, University of California, Berkeley (1991)Google Scholar
  24. 24.
    Jančar P.: Undecidability of bisimilarity for Petri nets and some related problems. Theor. Comput. Sci. 148(2), 281–301 (1995)zbMATHCrossRefGoogle Scholar
  25. 25.
    Khomenko, V.: Model Checking Based on Prefixes of Petri Net Unfoldings. PhD thesis, School of Computing Science, Newcastle University (2003)Google Scholar
  26. 26.
    Khomenko, V., Koutny, M., Niaouris, A.: Applying Petri net unfoldings for verification of mobile systems. In: Proc. of the 4th Workshop on Modelling of Objects, Components and Agents, MOCA. Bericht FBI-HH-B-267/06, pp. 161–178. University of Hamburg (2006)Google Scholar
  27. 27.
    Khomenko, V., Meyer, R.: Checking π-Calculus structural congruence is graph isomorphism complete. Technical Report CS-TR-1100, School of Computing Science, Newcastle University (2008). URL:
  28. 28.
    McMillan, K.: Using unfoldings to avoid the state explosion problem in the verification of asynchronous circuits. In: Proc. of the 4th International Workshop on Computer Aided Verification, CAV. LNCS, vol. 663, pp. 164–174. Springer, Heidelberg (1992)Google Scholar
  29. 29.
    Meyer, R.: On boundedness in depth in the π-calculus. In: Proc. of the 5th IFIP International Conference on Theoretical Computer Science, IFIP TCS. IFIP, vol. 273, pp. 477–489. Springer, Heidelberg (2008)Google Scholar
  30. 30.
    Milner R.: Communicating and Mobile Systems: the π-Calculus. Cambridge University Press, London (1999)Google Scholar
  31. 31.
    Meyer, R., Khomenko, V., Strazny, T.: A practical approach to verification of mobile systems using net unfoldings. In: Proc. of the 29th International Conference on Application and Theory of Petri Nets and Other Models of Concurrency, ATPN. LNCS, vol. 5062, pp. 327–347. Springer, Heidelberg (2008)Google Scholar
  32. 32.
    Montanari, U., Pistore, M.: Checking bisimilarity for finitary π-calculus. In: Proc. of the 6th International Conference on Concurrency Theory, CONCUR. LNCS, vol. 962, pp. 42–56. Springer, Heidelberg (1995)Google Scholar
  33. 33.
    Montanari U., Pistore M.: Concurrent semantics for the π-calculus. Electr. Notes Theor. Comput. Sci. 1, 411–429 (1995)CrossRefMathSciNetGoogle Scholar
  34. 34.
    Montanari, U., Pistore, M.: History dependent automata. Technical report, Instituto Trentino di Cultura (2001)Google Scholar
  35. 35.
    Olderog, E.-R.: Nets, Terms and Formulas: Three Views of Concurrent Processes and Their Relationship. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, London (1991)Google Scholar
  36. 36.
    Pistore, M.: History Dependent Automata. PhD thesis, Dipartimento di Informatica, Università di Pisa (1999)Google Scholar
  37. 37.
    Reisig, W.: Petri nets: an introduction. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Heidelberg (1985)Google Scholar
  38. 38.
    Strazny, T., Meyer, R.: Petruchio homepage. (2008)
  39. 39.
    Strazny, T.: Entwurf und Implementierung von Algorithmen zur Berechnung von Petrinetz-Semantiken für Pi-Kalkül-Prozesse. Master’s thesis, Department of Computing Science, University of Oldenburg (2007)Google Scholar
  40. 40.
    Sangiorgi D., Walker D.: The π-calculus: a Theory of Mobile Processes. Cambridge University Press, London (2001)Google Scholar
  41. 41.
    Victor, B., Moller, F.: The mobility workbench: a tool for the π-calculus. In: Proc. of the 6th International Conference on Computer Aided Verification. LNCS, vol. 818, pp. 428–440. Springer, Heidelberg (1994), Mobility Workbench:

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Computing ScienceUniversity of OldenburgOldenburgGermany

Personalised recommendations