Deriving Weak Bisimulation Congruences from Reduction Systems

  • Roberto Bruni
  • Fabio Gadducci
  • Ugo Montanari
  • Paweł Sobociński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3653)


The focus of process calculi is interaction rather than computation, and for this very reason: (i) their operational semantics is conveniently expressed by labelled transition systems (LTSs) whose labels model the possible interactions with the environment; (ii) their abstract semantics is conveniently expressed by observational congruences. However, many current-day process calculi are more easily equipped with reduction semantics, where the notion of observable action is missing. Recent techniques attempted to bridge this gap by synthesising LTSs whose labels are process contexts that enable reactions and for which bisimulation is a congruence. Starting from Sewell’s set-theoretic construction, category-theoretic techniques were defined and based on Leifer and Milner’s relative pushouts, later refined by Sassone and the fourth author to deal with structural congruences given as groupoidal 2-categories.

Building on recent works concerning observational equivalences for tile logic, the paper demonstrates that double categories provide an elegant setting in which the aforementioned contributions can be studied. Moreover, the formalism allows for a straightforward and natural definition of weak observational congruence.


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  1. 1.
    Bruni, R., de Frutos-Escrig, D., Martí-Oliet, N., Montanari, U.: Bisimilarity congruences for open terms and term graphs via tile logic. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 259–274. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Bruni, R., Meseguer, J., Montanari, U.: Symmetric and cartesian double categories as a semantic framework for tile logic. Mathematical Structures in Computer Science 12, 53–90 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bruni, R., Montanari, U., Rossi, F.: An interactive semantics of logic programming. Theory and Practice of Logic Programming 1, 647–690 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bruni, R., Montanari, U., Sassone, V.: Observational congruences for dynamically reconfigurable tile systems. Theor. Comp. Sci. 335(2-3), 331–372 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Corradini, A., Gadducci, F.: Rewriting on cyclic structures: Equivalence between the operational and the categorical description. Informatique Théorique et Applications/Theoretical Informatics and Applications 33, 467–493 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Ferrari, G., Montanari, U.: Tile formats for located and mobile systems. Inform. and Comput. 156, 173–235 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Gadducci, F., Heckel, R., Llabrés, M.: A bi-categorical axiomatisation of concurrent graph rewriting. In: Nickel, K. (ed.) Proc. of CTCS 1999. Electr. Notes in Theor. Comp. Sci, vol. 29, Elsevier, Amsterdam (1975)Google Scholar
  8. 8.
    Gadducci, F., Montanari, U.: The tile model. In: Proof, Language and Interaction: Essays in Honour of Robin Milner, pp. 133–166. MIT Press, Cambridge (2000)Google Scholar
  9. 9.
    Jensen, O.H.: Bigraphs and weak bisimilarity. Talk at Dagstuhl Seminar 04241 (June 2004) Google Scholar
  10. 10.
    Jensen, O.H., Milner, R.: Bigraphs and mobile processes. Technical Report 570, Computer Laboratory, University of Cambridge (2003) Google Scholar
  11. 11.
    Leifer, J., Milner, R.: Deriving bisimulation congruences for reactive systems. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 243–258. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  12. 12.
    Melliès, P.A.: Double categories: A modular model of multiplicative linear logic. Mathematical Structures in Computer Science 12, 449–479 (2002)zbMATHCrossRefGoogle Scholar
  13. 13.
    Meseguer, J.: Conditional rewriting logic as a unified model of concurrency. Theor. Comp. Sci. 96, 73–155 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Milner, R.: The polyadic π-calculus: A tutorial. In: Logic and Algebra of Specification. Nato ASI Series F, vol. 94, pp. 203–246. Springer, Heidelberg (1993)Google Scholar
  15. 15.
    Palmquist, P.H.: The double category of adjoint squares. In: Midwest Category Seminar. Lectures Notes in Mathematics, vol. 195, pp. 123–153. Springer, Heidelberg (1971)CrossRefGoogle Scholar
  16. 16.
    Power, A.J.: An abstract formulation for rewrite systems. In: Dybjer, P., Pitts, A.M., Pitt, D.H., Poigné, A., Rydeheard, D.E. (eds.) Category Theory and Computer Science. LNCS, vol. 389, pp. 300–312. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  17. 17.
    Rydehard, D.E., Stell, E.G.: Foundations of equational deductions: A categorical treatment of equational proofs and unification algorithms. In: Pitt, D.H., Rydeheard, D.E., Poigné, A. (eds.) Category Theory and Computer Science. LNCS, vol. 283, pp. 114–139. Springer, Heidelberg (1987)Google Scholar
  18. 18.
    Sassone, V., Sobociński, P.: Deriving bisimulation congruences using 2-categories. Nordic Journal of Computing 10, 163–183 (2003)zbMATHMathSciNetGoogle Scholar
  19. 19.
    Sewell, P.: From rewrite rules to bisimulation congruences. Theor. Comp. Sci. 274, 183–230 (2004)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Street, R.H.: Categorical structures. In: Handbook of Algebra, vol. 1, pp. 529–577. North-Holland, Amsterdam (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Roberto Bruni
    • 1
  • Fabio Gadducci
    • 1
  • Ugo Montanari
    • 1
  • Paweł Sobociński
    • 1
  1. 1.Dipartimento di InformaticaUniversità di PisaItalia

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