The Microcosm Principle and Compositionality of GSOS-Based Component Calculi

  • Ichiro Hasuo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6859)


In the previous work by Jacobs, Sokolova and the author, synchronous parallel composition of coalgebras—yielding a coalgebra—and parallel composition of behaviors—yielding a behavior, where behaviors are identified with states of the final coalgebra—were observed to form an instance of the microcosm principle. The microcosm principle, a term by Baez and Dolan, refers to the general phenomenon of nested algebraic structures such as a monoid in a monoidal category. Suitable organization of these two levels of parallel composition led to a general compositionality theorem: the behavior of the composed system relies only on the behaviors of its constituent parts. In the current paper this framework is extended so that it accommodates any process operator—not restricted to parallel composition—whose meaning is specified by means of GSOS rules. This generalizes Turi and Plotkin’s bialgebraic modeling of GSOS, by allowing a process operator to act as a connector between components as coalgebras.


State Space Natural Transformation Operational Semantic Regular Language Monoidal Category 
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.
    Aceto, L., Fokkink, W., Verhoef, C.: Structural operational semantics. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, pp. 197–292. Elsevier, Amsterdam (2001)Google Scholar
  2. 2.
    Baez, J.C., Dolan, J.: Higher dimensional algebra III: n-categories and the algebra of opetopes. Adv. Math. 135, 145–206 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Baier, C., Blechmann, T., Klein, J., Klüppelholz, S.: A uniform framework for modeling and verifying components and connectors. In: Field, J., Vasconcelos, V.T. (eds.) COORDINATION 2009. LNCS, vol. 5521, pp. 247–267. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Baier, C., Sirjani, M., Arbab, F., Rutten, J.J.M.M.: Modeling component connectors in reo by constraint automata. Science of Comput. Progr. 61(2), 75–113 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Bliudze, S., Krob, D.: Modelling of complex systems: Systems as dataflow machines. Fundam. Inform. 91(2), 251–274 (2009)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Bloom, B., Istrail, S., Meyer, A.R.: Bisimulation can’t be traced. Journ. ACM 42(1), 232–268 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Bonsangue, M.M., Clarke, D., Silva, A.: Automata for context-dependent connectors. In: Field, J., Vasconcelos, V.T. (eds.) COORDINATION 2009. LNCS, vol. 5521, pp. 184–203. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Bruni, R., Lanese, I., Montanari, U.: A basic algebra of stateless connectors. Theor. Comp. Sci. 366(1-2), 98–120 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  10. 10.
    Curien, P.L.: Operads, clones, and distributive laws, preprint, available online (2008)Google Scholar
  11. 11.
    Hasuo, I.: Tracing Anonymity with Coalgebras. Ph.D. thesis, Radboud Univ. Nijmegen (2008)Google Scholar
  12. 12.
    Hasuo, I.: The microcosm principle and compositionality of GSOS-based component calculi. Extended version with proofs, available online (May 2011)Google Scholar
  13. 13.
    Hasuo, I., Jacobs, B., Sokolova, A.: Generic trace semantics via coinduction. Logical Methods in Comp. Sci. 3(4:11) (2007)Google Scholar
  14. 14.
    Hasuo, I., Jacobs, B., Sokolova, A.: The microcosm principle and concurrency in coalgebra. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 246–260. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Jacobs, B.: Introduction to coalgebra. Towards mathematics of states and observations, Draft of a book (2005),
  16. 16.
    Klin, B.: Bialgebraic methods and modal logic in structural operational semantics. Inf. & Comp. 207(2), 237–257 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Klin, B.: Structural operational semantics for weighted transition systems. In: Palsberg, J. (ed.) Semantics and Algebraic Specification. LNCS, vol. 5700, pp. 121–139. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  18. 18.
    Lenisa, M., Power, J., Watanabe, H.: Category theory for operational semantics. Theor. Comp. Sci. 327(1-2), 135–154 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Martí-Oliet, N., Meseguer, J.: Rewriting logic: roadmap and bibliography. Theor. Comp. Sci. 285(2), 121–154 (2002)zbMATHCrossRefGoogle Scholar
  20. 20.
    Plotkin, G.D.: A structural approach to operational semantics, report DAIMI FN-19, Aarhus Univ. (1981)Google Scholar
  21. 21.
    Silva, A., Bonchi, F., Bonsangue, M.M., Rutten, J.J.M.M.: Quantitative kleene coalgebras. Inf. & Comp. 209(5), 822–849 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Turi, D., Plotkin, G.: Towards a mathematical operational semantics. In: Logic in Computer Science, pp. 280–291. IEEE, Computer Science Press (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ichiro Hasuo
    • 1
  1. 1.University of TokyoJapan

Personalised recommendations