Weak Bisimilarity Coalgebraically

  • Andrei Popescu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5728)


We argue that weak bisimilarity of processes can be conveniently captured in a semantic domain by a combination of traces and coalgebraic finality, in such a way that important process algebra aspects such as parallel composition and recursion can be represented compositionally. We illustrate the usefulness of our approach by providing a fully-abstract denotational semantics for CCS under weak bisimilarity.


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  1. 1.
    Abramsky, S.: A domain equation for bisimulation. Inf. Comput. 92(2), 161–218 (1991)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Aczel, P.: Final universes of processes. In: Main, M.G., Melton, A.C., Mislove, M.W., Schmidt, D., Brookes, S.D. (eds.) MFPS 1993. LNCS, vol. 802, pp. 1–28. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  3. 3.
    Baldamus, M., Parrow, J., Victor, B.: A fully abstract encoding of the pi-calculus with data terms. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1202–1213. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Baldamus, M., Stauner, T.: Modifying Esterel concepts to model hybrid systems. Electr. Notes Theor. Comput. Sci. 65(5) (2002)Google Scholar
  5. 5.
    Bloom, B.: Structural operational semantics for weak bisimulations. Theor. Comput. Sci., 146(1&2), 25–68 (1995)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Boreale, M., Gadducci, F.: Denotational testing semantics in coinductive form. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 279–289. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Buscemi, M.G., Montanari, U.: A first order coalgebraic model of π-calculus early observational equivalence. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 449–465. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Cattani, G.L., Sewell, P.: Models for name-passing processes: interleaving and causal. In: LICS 2000, pp. 322–333 (2000)Google Scholar
  9. 9.
    Fiore, M., Cattani, G.L., Winskel, G.: Weak bisimulation and open maps. In: LICS 1999, pp. 67–76 (1999)Google Scholar
  10. 10.
    Fiore, M.P., Moggi, E., Sangiorgi, D.: A fully-abstract model for the π-calculus. In: LICS 1996, pp. 43–54 (1996)Google Scholar
  11. 11.
    Hennessy, M.: A fully abstract denotational semantics for the π-calculus. Theor. Comput. Sci. 278(1-2), 53–89 (2002)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Honsell, F., Lenisa, M., Montanari, U., Pistore, M.: Final semantics for the pi-calculus. In: PROCOMET 1998, pp. 225–243 (1998)Google Scholar
  13. 13.
    Lenisa, M.: Themes in Final Semantics. Dipartimento di Informatica, Universita‘ di Pisa, TD 6 (1998)Google Scholar
  14. 14.
    Milner, R.: Communication and concurrency. Prentice-Hall, Englewood Cliffs (1989)MATHGoogle Scholar
  15. 15.
    Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, parts i and ii. Inf. Comput. 100(1), 1–77 (1992)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Nielsen, M., Chang, A.: Observe behaviour categorically. In: FST&TCS 1995, pp. 263–278 (1995)Google Scholar
  17. 17.
    Popescu, A.: A fully abstract coalgebraic semantics for the pi-calculus under weak bisimilarity. Tech. Report UIUCDCS-R-2009-3045. University of Illinois (2009)Google Scholar
  18. 18.
    Rutten, J.J.M.M.: Processes as terms: Non-well-founded models for bisimulation. Math. Struct. Comp. Sci. 2(3), 257–275 (1992)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Rutten, J.J.M.M.: Universal coalgebra: a theory of systems. Theor. Comput. Sci. 249(1), 3–80 (2000)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Sangiorgi, D., Walker, D.: The π-calculus. A theory of mobile processes. Cambridge (2001)Google Scholar
  21. 21.
    Sokolova, A., de Vink, E.P., Woracek, H.: Weak bisimulation for action-type coalgebras. Electr. Notes Theor. Comput. Sci. 122, 211–228 (2005)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Stark, I.: A fully-abstract domain model for the π-calculus. In: LICS 1996, pp. 36–42 (1996)Google Scholar
  23. 23.
    Staton, S.: Name-passing process calculi: operational models and structural operational semantics. PhD thesis, University of Cambridge (2007)Google Scholar
  24. 24.
    Turi, D., Plotkin, G.: Towards a mathematical operational semantics. In: LICS 1997, pp. 280–291 (1997)Google Scholar
  25. 25.
    van Glabbeek, R.J.: On cool congruence formats for weak bisimulations. In: Van Hung, D., Wirsing, M. (eds.) ICTAC 2005. LNCS, vol. 3722, pp. 318–333. Springer, Heidelberg (2005)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Andrei Popescu
    • 1
  1. 1.University of Illinois at Urbana-Champaign and Institute of Mathematics Simion Stoilow of the Romanian AcademyUSA

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