Generic Forward and Backward Simulations

  • Ichiro Hasuo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4137)


The technique of forward/backward simulations has been applied successfully in many distributed and concurrent applications. In this paper, however, we claim that the technique can actually have more genericity and mathematical clarity. We do so by identifying forward/backward simulations as lax/oplax morphisms of coalgebras. Starting from this observation, we present a systematic study of this generic notion of simulations. It is meant to be a generic version of the study by Lynch and Vaandrager, covering both non-deterministic and probabilistic systems. In particular we prove soundness and completeness results with respect to trace inclusion: the proof is by coinduction using the generic theory of traces developed by Jacobs, Sokolova and the author. By suitably instantiating our generic framework, one obtains the appropriate definition of forward/backward simulations for various kinds of systems, for which soundness and completeness come for free.


Start State Forward Simulation Shapely Functor Probabilistic Automaton Trace Semantic 
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  1. 1.
    Cheung, L.: Reconciling Nondeterministic and Probabilistic Choices. PhD thesis, Radboud Univ. Nijmegen (2006)Google Scholar
  2. 2.
    Fiore, M.: A coinduction principle for recursive data types based on bisimulation. Inf. & Comp. 127(2), 186–198 (1996)CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Garland, S., Lynch, N., Vaziri, M.: IOA: a language for specifying, programming, and validating distributed systems. MIT Laboratory for Computer Science, Cambridge (1997)Google Scholar
  4. 4.
    Hasuo, I., Jacobs, B.: Context-Free Languages via Coalgebraic Trace Semantics. In: Fiadeiro, J.L., Harman, N.A., Roggenbach, M., Rutten, J. (eds.) CALCO 2005. LNCS, vol. 3629, pp. 213–231. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Hasuo, I., Jacobs, B., Sokolova, A.: Generic trace theory. In: Coalgebraic Methods in Computer Science (CMCS 2006). Elect. Notes in Theor. Comp. Sci. Elsevier, Amsterdam (2006)Google Scholar
  6. 6.
    Hasuo, I.: Generic forward and backward simulations. Technical report, Research Center for Verification and Semantics, National Institute of Advanced Industrial Science and Technology (AIST), Japan (2006),
  7. 7.
    Hughes, J., Jacobs, B.: Simulations in coalgebra. Theor. Comp. Sci. 327(1-2), 71–108 (2004)CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    Jou, C., Smolka, S.: Equivalences, congruences and complete axiomatizations for probabilistic processes. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 367–383. Springer, Heidelberg (1990)Google Scholar
  9. 9.
    Kawabe, Y., Mano, K., Sakurada, H., Tsukada, Y.: Backward simulations for anonymity. In: International Workshop on Issues in the Theory of Security (WITS 2006) (2006)Google Scholar
  10. 10.
    Kinoshita, Y., Power, J.: Data refinement and algebraic structure. Acta Informatica 36, 693–719 (2000)CrossRefMathSciNetMATHGoogle Scholar
  11. 11.
    Klarlund, N., Schneider, F.: Verifying safety properties using infinite-state automata. Technical Report 89-1039, Department of Computer Science, Cornell University, Ithaca, New York (1989)Google Scholar
  12. 12.
    Lynch, N., Vaandrager, F.: Forward and backward simulations. I. Untimed systems. Inf. & Comp. 121(2), 214–233 (1995)CrossRefMathSciNetMATHGoogle Scholar
  13. 13.
    Power, J., Turi, D.: A coalgebraic foundation for linear time semantics. In: Category Theory and Computer Science. Elect. Notes in Theor. Comp. Sci, vol. 29. Elsevier, Amsterdam (1999)Google Scholar
  14. 14.
    Rutten, J.: Universal coalgebra: a theory of systems. Theor. Comp. Sci. 249, 3–80 (2000)CrossRefMathSciNetMATHGoogle Scholar
  15. 15.
    Segala, R., Lynch, N.: Probabilistic simulations for probabilistic processes. Nordic Journ. Comput. 2(2), 250–273 (1995)MathSciNetMATHGoogle Scholar
  16. 16.
    Sokolova, A.: Coalgebraic Analysis of Probabilistic Systems. PhD thesis, TU Eindhoven (2005)Google Scholar
  17. 17.
    van Glabbeek, R., Smolka, S., Steffen, B.: Reactive, generative, and stratified models of probabilistic processes. Inf. & Comp. 121, 59–80 (1995)CrossRefMATHGoogle Scholar
  18. 18.
    Wu, S.H., Smolka, S.A., Stark, E.W.: Composition and behaviors of probabilistic I/O automata. Theor. Comp. Sci. 176(1–2), 1–38 (1997)CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ichiro Hasuo
    • 1
  1. 1.Institute for Computing and Information SciencesRadboud University NijmegenThe Netherlands

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