On Unique Decomposition of Processes in the Applied π-Calculus

  • Jannik Dreier
  • Cristian Ene
  • Pascal Lafourcade
  • Yassine Lakhnech
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7794)


Unique decomposition has been a subject of interest in process algebra for a long time (for example in BPP [2] or CCS [11,13]), as it provides a normal form with useful cancellation properties. We provide two parallel decomposition results for subsets of the Applied π-Calculus: we show that any closed normed (i.e. with a finite shortest complete trace) process P can be decomposed uniquely into prime factors P i with respect to strong labeled bisimilarity, i.e. such that P ~ l P 1 | …| P n . We also prove that closed finite processes can be decomposed uniquely with respect to weak labeled bisimilarity.


Applied π-Calculus Unique Decomposition Normal Form Weak Bisimilarity Strong Bisimilarity Factorization Cancellation 


  1. 1.
    Abadi, M., Fournet, C.: Mobile values, new names, and secure communication. In: Proceedings of the 28th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2001, pp. 104–115. ACM, New York (2001)CrossRefGoogle Scholar
  2. 2.
    Christensen, S.: Decidability and Decompostion in Process Algebras. PhD thesis, School of Computer Science, University of Edinburgh (1993)Google Scholar
  3. 3.
    Dreier, J., Lafourcade, P., Lakhnech, Y.: Defining Privacy for Weighted Votes, Single and Multi-voter Coercion. In: Foresti, S., Yung, M., Martinelli, F. (eds.) ESORICS 2012. LNCS, vol. 7459, pp. 451–468. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Dreier, J., Lafourcade, P., Lakhnech, Y.: On parallel factorization of processes in the applied pi calculus. Technical Report TR-2012-3, Verimag Research Report (March 2012),
  5. 5.
    Groote, J.F., Moller, F.: Verification of Parallel Systems via Decomposition. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 62–76. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  6. 6.
    Hirschkoff, D., Pous, D.: On Bisimilarity and Substitution in Presence of Replication. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 454–465. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Liu, J.: A proof of coincidence of labeled bisimilarity and observational equivalence in applied pi calculus. Technical Report ISCAS-SKLCS-11-05 (2011),
  8. 8.
    Luttik, B.: Unique parallel decomposition in branching and weak bisimulation semantics. Technical report (2012),
  9. 9.
    Luttik, B., van Oostrom, V.: Decomposition orders – another generalisation of the fundamental theorem of arithmetic. Theoretical Computer Science 335(2-3), 147–186 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Milner, R.: Communication and Concurrency. International Series in Computer Science. Prentice Hall (1989)Google Scholar
  11. 11.
    Milner, R., Moller, F.: Unique decomposition of processes. Theoretical Computer Science 107(2), 357–363 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes. Information and Computation 100(1), 1–40 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Moller, F.: Axioms for Concurrency. PhD thesis, School of Computer Science, University of Edinburgh (1989)Google Scholar
  14. 14.
    Nestmann, U., Pierce, B.C.: Decoding choice encodings. Information and Computation 163(1), 1–59 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Palamidessi, C., Herescu, O.M.: A randomized encoding of the pi-calculus with mixed choice. Theoretical Computer Science 335(23), 373–404 (2005)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jannik Dreier
    • 1
  • Cristian Ene
    • 1
  • Pascal Lafourcade
    • 1
  • Yassine Lakhnech
    • 1
  1. 1.Université Grenoble 1, CNRSVerimagFrance

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