Skip to main content

Relating Modal Refinements, Covariant-Contravariant Simulations and Partial Bisimulations

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNPSE,volume 7141)

Abstract

This paper studies the relationships between three notions of behavioural preorder that have been proposed in the literature: refinement over modal transition systems, and the covariant-contravariant simulation and the partial bisimulation preorders over labelled transition systems. It is shown that there are mutual translations between modal transition systems and labelled transition systems that preserve, and reflect, refinement and the covariant-contravariant simulation preorder. The translations are also shown to preserve the modal properties that can be expressed in the logics that characterize those preorders. A translation from labelled transition systems modulo the partial bisimulation preorder into the same model modulo the covariant-contravariant simulation preorder is also offered, together with some evidence that the former model is less expressive than the latter. In order to gain more insight into the relationships between modal transition systems modulo refinement and labelled transition systems modulo the covariant-contravariant simulation preorder, their connections are also phrased and studied in the context of institutions.

Keywords

  • Modal Logic
  • Transition System
  • Supervisory Control
  • Label Transition System
  • Modal Formula

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.

Research supported by Spanish projects DESAFIOS10 TIN2009-14599-C03-01, TESIS TIN2009-14321-C02-01 and PROMETIDOS S2009/TIC-1465, the project ‘Processes and Modal Logics’ (project nr. 100048021) of the Icelandic Fund for Research, and the Abel Extraordinary Chair programme within the NILS Mobility Project.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Antonik, A., Huth, M., Larsen, K.G., Nyman, U., Wąsowski, A.: 20 years of modal and mixed specifications. Bull. Eur. Assoc. Theor. Comput. Sci. EATCS 95, 94–129 (2008)

    MATH  Google Scholar 

  2. Baeten, J., van Beek, D., Luttik, B., Markovski, J., Rooda, J.: Partial bisimulation. SE Report 2010-04, Systems Engineering Group, Department of Mechanical Engineering, Eindhoven University of Technology (2010)

    Google Scholar 

  3. Boudol, G., Larsen, K.G.: Graphical versus logical specifications. Theoretical Comput. Sci. 106(1), 3–20 (1992)

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Darondeau, P., Dubreil, J., Marchand, H.: Supervisory control for modal specifications of services. In: Proceedings of WODES 2010, Berlin, Germany, August 30–September 1 (2010) (to appear)

    Google Scholar 

  5. Fábregas, I., de Frutos Escrig, D., Palomino, M.: Non-Strongly Stable Orders also Define Interesting Simulation Relations. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds.) CALCO 2009. LNCS, vol. 5728, pp. 221–235. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  6. Fábregas, I., de Frutos Escrig, D., Palomino, M.: Logics for Contravariant Simulations. In: Hatcliff, J., Zucca, E. (eds.) FMOODS/ FORTE 2010. LNCS, vol. 6117, pp. 224–231. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  7. Fecher, H., de Frutos-Escrig, D., Lüttgen, G., Schmidt, H.: On the Expressiveness of Refinement Settings. In: Arbab, F., Sirjani, M. (eds.) FSEN 2009. LNCS, vol. 5961, pp. 276–291. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  8. Feuillade, G., Pinchinat, S.: Modal specifications for the control theory of discrete event systems. Discrete Event Dynamical Systems 17, 211–232 (2007)

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Goguen, J.A., Burstall, R.M.: Institutions: Abstract model theory for specification and programming. J. ACM 39(1), 95–146 (1992)

    MathSciNet  MATH  Google Scholar 

  10. Graf, S., Sifakis, J.: A modal characterization of observational congruence on finite terms of CCS. Information and Control 68(1–3), 125–145 (1986)

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Larsen, K.G.: Modal Specifications. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 232–246. Springer, Heidelberg (1990)

    CrossRef  Google Scholar 

  12. Larsen, K.G., Thomsen, B.: A modal process logic. In: Proceedings of 3rd Annual Symposium on Logic in Computer Science, Edinburgh, pp. 203–210. IEEE Computer Society Press (1988)

    Google Scholar 

  13. Milner, R.: Communication and Concurrency. Prentice-Hall International, Englewood Cliffs (1989)

    MATH  Google Scholar 

  14. Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)

    CrossRef  Google Scholar 

  15. Ramadge, P., Wonham, W.: Supervisory control of a class of discrete event processes. SIAM Journal of Control and Optimization 25, 206–230 (1987)

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Steffen, B., Ingólfsdóttir, A.: Characteristic formulae for processes with divergence. Information and Computation 110(1), 149–163 (1994)

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Aceto, L., Fábregas, I., de Frutos Escrig, D., Ingólfsdóttir, A., Palomino, M. (2012). Relating Modal Refinements, Covariant-Contravariant Simulations and Partial Bisimulations. In: Arbab, F., Sirjani, M. (eds) Fundamentals of Software Engineering. FSEN 2011. Lecture Notes in Computer Science, vol 7141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29320-7_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29320-7_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29319-1

  • Online ISBN: 978-3-642-29320-7

  • eBook Packages: Computer ScienceComputer Science (R0)