Nothing Special   »   [go: up one dir, main page]

Skip to main content

Model Refinement Using Bisimulation Quotients

  • Conference paper
Algebraic Methodology and Software Technology (AMAST 2010)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6486))

Abstract

The paper shows how to refine large-scale or even infinite transition systems so as to ensure certain desired properties. First, a given system is reduced into a smallish, finite bisimulation quotient. Second, the reduced system is refined in order to ensure a given property, using any known finite-state method. Third, the refined reduced system is expanded back into an adequate refinement of the system given initially. The proposed method is based on a Galois connection between systems and their quotients. It is applicable to various models and bisimulations and is illustrated with a few qualitative and quantitative properties.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Baier, C., Katoen, J.-P.: Principles of model checking. MIT Press, Cambridge (2008)

    MATH  Google Scholar 

  2. Clarke, E., Grumberg, O., Peled, D.: Model checking, 3rd edn. MIT Press, Cambridge (2001)

    Google Scholar 

  3. Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: 4th Symp. Principles of Programming Languages, pp. 238–252. ACM, New York (1977)

    Google Scholar 

  4. Erné, M., Koslowski, J., Melton, A., Strecker, G.: A primer on Galois connections. In: Andima, S., et al. (eds.) Papers on general topology and its applications. 7th Summer Conf. Wisconsin. Annals New York Acad. Sci., New York, 704th edn., pp. 103–125 (1994)

    Google Scholar 

  5. Fernandez, J.-C.: An implementation of an efficient algorithm for bisimulation equivalence. Sci. Computer Programming 13(2-3), 219–236 (1989)

    MathSciNet  MATH  Google Scholar 

  6. Foster, J.N., Greenwald, M.B., Moore, J.T., Pierce, B.J., Schmitt, A.: Combinators for bidirectional tree transformations: a linguistic approach to the view-update problem. ACM Trans. Programming Languages and Systems  29(3), Article 17, 17–65 (2007)

    Google Scholar 

  7. Givan, R., Dean, T., Greig, M.: Equivalence notions and model minimization in Markov decision processes. Artificial Intell. J. 147(1-2), 163–223 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. 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)

    Chapter  Google Scholar 

  9. Gondran, M., Minoux, M.: Graphs, dioids and semirings: new models and algorithms. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  10. Henzinger, T.A., Majumdar, R., Raskin, J.-F.: A classification of symbolic transition systems. ACM Trans. Computational Logic 6, 1–32 (2005)

    Article  MathSciNet  Google Scholar 

  11. Kanellakis, P., Smolka, S.: CCS expressions, finite state processes, and three problems of equivalence. Information and Computation 86, 43–68 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  12. Marchand, H., Pinchinat, S.: Supervisory control problem using symbolic bisimulation techniques. In: Proc. Amer. Control Conf., vol. 6, pp. 4067–4071 (2000)

    Google Scholar 

  13. Milner, R.: A calculus of communicating systems. Extended reprint of LNCS 92. University of Edinburgh, Laboratory for Foundations of Computer Science, Report ECS-LFCS-86-7 (1986)

    Google Scholar 

  14. Milner, R.: Operational and algebraic semantics of concurrent processes. In: van Leeuwen, J. (ed.) Formal models and semantics. Handbook of Theoretical Computer Sci., vol. B, pp. 1201–1242. Elsevier, Amsterdam (1990)

    Google Scholar 

  15. 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)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Glück, R., Möller, B., Sintzoff, M. (2011). Model Refinement Using Bisimulation Quotients. In: Johnson, M., Pavlovic, D. (eds) Algebraic Methodology and Software Technology. AMAST 2010. Lecture Notes in Computer Science, vol 6486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17796-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-17796-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17795-8

  • Online ISBN: 978-3-642-17796-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics