Trace Semantics via Generic Observations

  • Sergey Goncharov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8089)

Abstract

Recent progress on defining abstract trace semantics for coalgebras rests upon two observations: (i) coalgebraic bisimulation for deterministic automata coincides with trace equivalence, and (ii) the classical powerset construction for automata determinization instantiates the generic idea of lifting a functor to the Eilenberg-Moore category of an appropriate monad \(\mathbb{T}\). We take this approach one step further by rebasing the latter kind of trace semantics on the novel notion of \(\mathbb{T}\)-observer, which is just a certain natural transformation of the form F → GT, and thus allowing for elimination of assumptions about the structure of the coalgebra functor. As a specific application of this idea we demonstrate how it can be used for capturing trace semantics of push-down automata. Furthermore, we show how specific forms of observers can be used for coalgebra-based treatment of internal automata transitions as well as weak bisimilarity of processes.

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References

  1. 1.
    Adámek, J., Herrlich, H., Strecker, G.: Abstract and concrete categories. John Wiley & Sons Inc., New York (1990)MATHGoogle Scholar
  2. 2.
    Baeten, J.C.M., Luttik, B., van Tilburg, P.: Reactive turing machines. In: Owe, O., Steffen, M., Telle, J.A. (eds.) FCT 2011. LNCS, vol. 6914, pp. 348–359. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    Barbosa, L.S.: Towards a calculus of state-based software components. Journal of Universal Comp. Sci. 9, 891–909 (2003)Google Scholar
  4. 4.
    Bonsangue, M.M., Milius, S., Silva, A.: Sound and complete axiomatizations of coalgebraic language equivalence. ACM Trans. Comp. Logic 14(1), 7:1–7:7 (2013)Google Scholar
  5. 5.
    Dubuc, E.: Kan Extensions in Enriched Category Theory. LNM, vol. 145 (1970)Google Scholar
  6. 6.
    Fiore, M., Cattani, G.L., Winskel, G.: Weak bisimulation and open maps. In: LICS 1999 (1999)Google Scholar
  7. 7.
    Goncharov, S., Schröder, L.: A coinductive calculus for asynchronous side-effecting processes. In: Owe, O., Steffen, M., Telle, J.A. (eds.) FCT 2011. LNCS, vol. 6914, pp. 276–287. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    Goncharov, S., Schröder, L.: Powermonads and tensors of unranked effects. In: LICS 2011, pp. 227–236 (2011)Google Scholar
  9. 9.
    Hasuo, I., Jacobs, B., Sokolova, A.: Generic trace theory. In: CMCS 2006. Elect. Notes in Theor. Comp. Sci., vol. 164, pp. 47–65. Elsevier (2006)Google Scholar
  10. 10.
    Hyland, M., Plotkin, G., Power, J.: Combining computational effects: Commutativity & Sum. In: TCS 2002, vol. 223, pp. 474–484. Kluwer (2002)Google Scholar
  11. 11.
    Jacobs, B.: Trace semantics for coalgebras. Electron. Notes Theor. Comput. Sci. 106, 167–184 (2004)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Jacobs, B., Poll, E.: Coalgebras and Monads in the Semantics of Java. Theoret. Comput. Sci. 291, 329–349 (2003)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Jacobs, B., Silva, A., Sokolova, A.: Trace semantics via determinization. In: Pattinson, D., Schröder, L. (eds.) CMCS 2012. LNCS, vol. 7399, pp. 109–129. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Klin, B.: Bialgebras for structural operational semantics: An introduction. Theor. Comput. Sci. 412(38), 5043–5069 (2011)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Kock, A.: Strong functors and monoidal monads. Archiv der Mathematik 23(1), 113–120 (1972)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Mac Lane, S.: Categories for the Working Mathematician. Springer (1971)Google Scholar
  17. 17.
    Milner, R.: Communication and concurrency. Prentice-Hall, Inc., Upper Saddle River (1989)MATHGoogle Scholar
  18. 18.
    Moggi, E.: A modular approach to denotational semantics. In: Curien, P.-L., Pitt, D.H., Pitts, A.M., Poigné, A., Rydeheard, D.E., Abramsky, S. (eds.) CTCS 1991. LNCS, vol. 530, pp. 138–139. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  19. 19.
    Moggi, E.: Notions of computation and monads. Inf. Comput. 93, 55–92 (1991)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Pavlovic, D., Mislove, M., Worrell, J.B.: Testing semantics: Connecting processes and process logics. In: Johnson, M., Vene, V. (eds.) AMAST 2006. LNCS, vol. 4019, pp. 308–322. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  21. 21.
    Plotkin, G., Power, J.: Adequacy for algebraic effects. In: Honsell, F., Miculan, M. (eds.) FOSSACS 2001. LNCS, vol. 2030, pp. 1–24. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  22. 22.
    Plotkin, G., Power, J.: Notions of computation determine monads. In: Nielsen, M., Engberg, U. (eds.) FOSSACS 2002. LNCS, vol. 2303, pp. 342–356. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  23. 23.
    Plotkin, G., Power, J.: Algebraic operations and generic effects. Appl. Cat. Struct. 11, 69–94 (2003)MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Power, J., Shkaravska, O.: From comodels to coalgebras: State and arrays. In: CMCS 2004. ENTCS, vol. 106, pp. 297–314 (2004)Google Scholar
  25. 25.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of formal languages. Word, Language, Grammar, vol. 1. Springer-Verlag New York, Inc. (1997)Google Scholar
  26. 26.
    Rutten, J.: Universal coalgebra: A theory of systems. Theoret. Comput. Sci. 249, 3–80 (2000)MathSciNetMATHCrossRefGoogle Scholar
  27. 27.
    Rutten, J.J.M.M.: Algebraic specification and coalgebraic synthesis of mealy automata. Electr. Notes Theor. Comput. Sci. 160, 305–319 (2006)CrossRefGoogle Scholar
  28. 28.
    Silva, A., Bonchi, F., Bonsangue, M., Rutten, J.: Generalizing determinization from automata to coalgebras. LMCS 9(1) (2013)Google Scholar
  29. 29.
    Silva, A., Sokolova, A.: Sound and complete axiomatization of trace semantics for probabilistic systems. Electr. Notes Theor. Comput. Sci. 276, 291–311 (2011)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Uustalu, T., Vene, V.: Comonadic notions of computation. Electron. Notes Theor. Comput. Sci. 203(5), 263–284 (2008)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sergey Goncharov
    • 1
  1. 1.Department of Computer ScienceFriedrich-Alexander-Universität Erlangen-NürnbergGermany

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