Structural Operational Semantics for Weighted Transition Systems

  • Bartek Klin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5700)


Weighted transition systems are defined, parametrized by a commutative monoid of weights. These systems are further understood as coalgebras for functors of a specific form. A general rule format for the SOS specification of weighted systems is obtained via the coalgebraic approach of Turi and Plotkin. Previously known formats for labelled transition systems (GSOS) and stochastic systems (SGSOS) appear as special cases.


Transition System Natural Transformation Operational Semantic Label Transition System Commutative Monoid 
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  1. 1.
    Aceto, L., Fokkink, W.J., Verhoef, C.: Structural operational semantics. In: Bergstra, J.A., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, pp. 197–292. Elsevier, Amsterdam (2002)Google Scholar
  2. 2.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1988)zbMATHGoogle Scholar
  3. 3.
    Bloom, B., Istrail, S., Meyer, A.: Bisimulation can’t be traced. Journal of the ACM 42, 232–268 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Plotkin, G.D.: A structural approach to operational semantics. DAIMI Report FN-19, Computer Science Department, Aarhus University (1981)Google Scholar
  5. 5.
    Plotkin, G.D.: A structural approach to operational semantics. Journal of Logic and Algebraic Programming 60-61, 17–139 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Sangiorgi, D., Walker, D.: The π-Calculus: a Theory of Mobile Processes. Cambridge University Press, Cambridge (2003)Google Scholar
  7. 7.
    Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Information and Computation 94, 1–28 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Moller, F., Tofts, C.: A temporal calculus of communicating systems. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 401–415. Springer, Heidelberg (1990)Google Scholar
  9. 9.
    Mosses, P.D.: Foundations of Modular SOS. In: Kutyłowski, M., Wierzbicki, T., Pacholski, L. (eds.) MFCS 1999. LNCS, vol. 1672, pp. 70–80. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  10. 10.
    Mosses, P.D.: Modular structural operational semantics. Journal of Logic and Algebraic Programming 60-61, 195–228 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Rutten, J.J.M.M.: Universal coalgebra: a theory of systems. Theoretical Computer Science 249, 3–80 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Turi, D., Plotkin, G.D.: Towards a mathematical operational semantics. In: Proc. LICS 1997, pp. 280–291. IEEE Computer Society Press, Los Alamitos (1997)Google Scholar
  13. 13.
    Bartels, F.: On Generalised Coinduction and Probabilistic Specification Formats. PhD dissertation, CWI, Amsterdam (2004)Google Scholar
  14. 14.
    Kick, M.: Rule formats for timed processes. In: Proc. CMCIM 2002. ENTCS, vol. 68, pp. 12–31. Elsevier, Amsterdam (2002)Google Scholar
  15. 15.
    Klin, B., Sassone, V.: Structural operational semantic for stochastic systems. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 428–442. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Kick, M., Power, J., Simpson, A.: Coalgebraic semantics for timed processes. Information and Computation 204, 588–609 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Lenisa, M., Power, J., Watanabe, H.: Category theory for operational semantics. Theoretical Computer Science 327(1-2), 135–154 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Mac Lane, S.: Categories for the Working Mathematician, 2nd edn. Springer, Heidelberg (1998)zbMATHGoogle Scholar
  19. 19.
    Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press, Cambridge (1996)CrossRefzbMATHGoogle Scholar
  20. 20.
    Klin, B.: Bialgebraic methods and modal logic in structural operational semantics. Information and Computation 207, 237–257 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Barr, M.: Terminal coalgebras in well-founded set theory. Theoretical Computer Science 114, 299–315 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    de Vink, E.P., Rutten, J.J.M.M.: Bisimulation for probabilistic transition systems: A coalgebraic approach. Theoretical Computer Science 221(1-2), 271–293 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Moss, L.: Coalgebraic logic. Annals of Pure and Applied Logic 96, 177–317 (1999)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Bartek Klin
    • 1
  1. 1.Warsaw University, University of CambridgePoland

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