A Categorical Approach to Simulations

  • Miguel Palomino
  • José Meseguer
  • Narciso Martí-Oliet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3629)


Simulations are a very natural way of relating concurrent systems, which are mathematically modeled by Kripke structures. The range of available notions of simulations makes it very natural to adopt a categorical viewpoint in which Kripke structures become the objects of several categories while the morphisms are obtained from the corresponding notion of simulation. Here we define in detail several of those categories, collect them together in various institutions, and study their most interesting properties.


Transition System Temporal Logic Categorical Approach Atomic Proposition Label Function 
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.


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  1. 1.
    Arrais, M., Fiadeiro, J.L.: Unifying theories in different institutions. In: Haveraaen, M., Dahl, O.-J., Owe, O. (eds.) Abstract Data Types 1995 and COMPASS 1995. LNCS, vol. 1130, pp. 81–101. Springer, Heidelberg (1996)Google Scholar
  2. 2.
    Barr, M., Wells, C.: Category Theory for Computing Science. 3rd edn. Centre de Recherches Mathématiques (1999)Google Scholar
  3. 3.
    Browne, M.C., Clarke, E.M., Grümberg, O.: Characterizing finite Kripke structures in propositional temporal logic. Theoretical Computer Science 59, 115–131 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Clarke, E.M., Grumberg, O., Long, D.E.: Model checking and abstraction. ACM Transactions on Programming Languages and Systems 16(5), 1512–1542 (1994)CrossRefGoogle Scholar
  5. 5.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  6. 6.
    Goguen, J., Burstall, R.: Institutions: Abstract model theory for specification and programming. Journal of the Association for Computing Machinery 39(1), 95–146 (1992)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Herrlich, H., Strecker, G.E.: Category Theory: An Introduction. Advanced Mathematics. Allyn and Bacon, Boston (1973)Google Scholar
  8. 8.
    Jacobs, B.: Categorical Logic and Type Theory. Studies in Logic and the Foundations of Mathematics, vol. 141. North-Holland, Amsterdam (1999)zbMATHGoogle Scholar
  9. 9.
    Mac Lane, S.: Categories for the Working Mathematician, 2nd edn. Springer, Heidelberg (1998)zbMATHGoogle Scholar
  10. 10.
    Manolios, P.: Mechanical Verification of Reactive Systems. PhD thesis, University of Texas at Austin (Aug. 2001)Google Scholar
  11. 11.
    Martí-Oliet, N., Meseguer, J., Palomino, M.: Theoroidal maps as algebraic simulations. In: Fiadeiro, J.L., Mosses, P.D., Orejas, F. (eds.) WADT 2004. LNCS, vol. 3423, pp. 126–143. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Martí-Oliet, N., Meseguer, J., Palomino, M.: Algebraic simulations. Submitted (2005),
  13. 13.
    Meseguer, J., Martí-Oliet, N., Palomino, M.: Equational abstractions. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 2–16. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Namjoshi, K.S.: A simple characterization of stuttering bisimulation. In: Ramesh, S., Sivakumar, G. (eds.) FST TCS 1997. LNCS, vol. 1346, pp. 284–296. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  15. 15.
    Tarlecki, A., Burstall, R.M., Goguen, J.A.: Some fundamental algebraic tools for the semantics of computation. Part 3: Indexed categories. Theoretical Computer Science 91(2), 239–264 (1991)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Miguel Palomino
    • 1
  • José Meseguer
    • 2
  • Narciso Martí-Oliet
    • 1
  1. 1.Departamento de Sistemas InformáticosUniversidad Complutense de Madrid 
  2. 2.Computer Science DepartmentUniversity of Illinois at Urbana-Champaign 

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