Using Bisimulations for Optimality Problems in Model Refinement

  • Roland Glück
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6663)

Abstract

A known generic strategy for handling large transition systems is the combined use of bisimulations and refinement. The idea is to reduce a large system by means of a bisimulation quotient into a smaller one, then to refine the smaller one in such way that it fulfils a desired property, and then to expand this refined system back into a submodel of the original one. This generic algorithm is not guaranteed to work correctly for every desired property; here we show its correctness for a class of optimality problems which can be described in the framework of dioids.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ahuja, R.K., Magnati, T.L., Orlin, J.B.: Network Flows. Prentice-Hall, Englewood Cliffs (1993)Google Scholar
  2. 2.
    Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press, Cambridge (2008)MATHGoogle Scholar
  3. 3.
    Billings, J.N., Griffin, T.G.: A model of internet routing using semi-modules. In: Berghammer, R., Jaoua, A.M., Möller, B. (eds.) RelMiCS 2009. LNCS, vol. 5827, pp. 29–43. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Esparza, J., Kiefer, S., Luttenberger, M.: Derivation tree analysis for accelerated fixed-point computation. In: Ito, M., Toyama, M. (eds.) DLT 2008. LNCS, vol. 5257, pp. 301–313. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Glück, R., Möller, B., Sintzoff, M.: A semiring approach to equivalences, bisimulations and control. In: Berghammer, R., Jaoua, A.M., Möller, B. (eds.) RelMiCS 2009. LNCS, vol. 5827, pp. 134–149. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Glück, R., Möller, B., Sintzoff, M.: Model refinement using bisimulation quotients. In: Johnson, M., Pavlovic, D. (eds.) AMAST 2010. LNCS, vol. 6486, pp. 76–91. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Gondran, M., Minoux, M.: Graphs, Dioids and Semirings. Springer, Heidelberg (2008)MATHGoogle Scholar
  8. 8.
    Höfner, P., Struth, G.: Automated reasoning in kleene algebra. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 279–294. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Jungnickel, D.: Graphs, Networks and Algorithms, 2nd edn. Springer, Heidelberg (2005)MATHGoogle Scholar
  10. 10.
    Kawahara, Y.: On the cardinality of relations. In: Schmidt, R.A. (ed.) RelMiCS/AKA 2006. LNCS, vol. 4136, pp. 251–265. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Myhill, J.: Finite automata and the representation of events. WADD TR-57-624, 112–137 (1957)Google Scholar
  12. 12.
    Nerode, A.: Linear automaton transformations. Proceedings of the American Mathematical Society 9, 541–544 (1958)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Paige, R., Tarjan, R.: Three partition refinement algorithms. SIAM Journal for Computing 16(6)Google Scholar
  14. 14.
    Sintzoff, M.: Synthesis of optimal control policies for some infinite-state transition systems. In: Audebaud, P., Paulin-Mohring, C. (eds.) MPC 2008. LNCS, vol. 5133, pp. 336–359. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Winter, M.: A relation-algebraic theory of bisimulations. Fundam. Inf. 83(4), 429–449 (2008)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Roland Glück
    • 1
  1. 1.Institut für InformatikUniversität AugsburgAugsburgGermany

Personalised recommendations