Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Automated Technology for Verification and Analysis

ATVA 2011: Automated Technology for Verification and Analysis pp 228–242Cite as

Modal Transition Systems: Composition and LTL Model Checking

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6996))

Abstract

Modal transition systems (MTS) is a well established formalism used for specification and for abstract interpretation. We consider its disjunctive extension (DMTS) and we provide algorithms showing that refinement problems for DMTS are not harder than in the case of MTS. There are two main results in the paper. Firstly, we identify an error in a previous attempt at LTL model checking of MTS and provide algorithms for LTL model checking of MTS and DMTS. Moreover, we show how to apply this result to compositional verification and circumvent the general incompleteness of the MTS composition. Secondly, we give a solution to the common implementation and conjunctive composition problems lowering the complexity from EXPTIME to PTIME.

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

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Larsen, K.G., Nyman, U., Wasowski, A.: Modeling software product lines using color-blind transition systems. STTT 9(5-6), 471–487 (2007)

    Article  Google Scholar 

  2. Larsen, K.G., Thomsen, B.: A modal process logic. In: LICS, pp. 203–210. IEEE Computer Society, Los Alamitos (1988)

    Google Scholar 

  3. Antonik, A., Huth, M., Larsen, K.G., Nyman, U., Wasowski, A.: 20 years of modal and mixed specifications. Bulletin of the EATCS (95), 94–129 (2008)

    Google Scholar 

  4. Raclet, J.B.: Residual for component specifications. In: Proc. of the 4th International Workshop on Formal Aspects of Component Software (2007)

    Google Scholar 

  5. Bertrand, N., Pinchinat, S., Raclet, J.B.: Refinement and consistency of timed modal specifications. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds.) LATA 2009. LNCS, vol. 5457, pp. 152–163. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. Raclet, J.B., Badouel, E., Benveniste, A., Caillaud, B., Passerone, R.: Why are modalities good for interface theories? In: ACSD, pp. 119–127. IEEE, Los Alamitos (2009)

    Google Scholar 

  7. Uchitel, S., Chechik, M.: Merging partial behavioural models. In: Proc. of FSE 2004, pp. 43–52. ACM, New York (2004)

    Google Scholar 

  8. Huth, M., Jagadeesan, R., Schmidt, D.A.: Modal transition systems: A foundation for three-valued program analysis. In: Sands, D. (ed.) ESOP 2001. LNCS, vol. 2028, pp. 155–169. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Godefroid, P., Huth, M., Jagadeesan, R.: Abstraction-based model checking using modal transition systems. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 426–440. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  10. Nanz, S., Nielson, F., Nielson, H.R.: Modal abstractions of concurrent behaviour. In: Alpuente, M., Vidal, G. (eds.) SAS 2008. LNCS, vol. 5079, pp. 159–173. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Larsen, K.G., Xinxin, L.: Equation solving using modal transition systems. In: LICS, pp. 108–117. IEEE Computer Society, Los Alamitos (1990)

    Google Scholar 

  12. Fecher, H., Steffen, M.: Characteristic mu-calculus formulas for underspecified transition systems. ENTCS 128(2), 103–116 (2005)

    MATH  Google Scholar 

  13. Fecher, H., Schmidt, H.: Comparing disjunctive modal transition systems with an one-selecting variant. J. of Logic and Alg. Program. 77(1-2), 20–39 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Antonik, A., Huth, M., Larsen, K.G., Nyman, U., Wasowski, A.: EXPTIME-complete decision problems for mixed and modal specifications. In: 15th International Workshop on Expressiveness in Concurrency (2008)

    Google Scholar 

  15. Beneš, N., Křetínský, J., Larsen, K., Srba, J.: On determinism in modal transition systems. Theoretical Computer Science 410(41), 4026–4043 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Juhl, L., Larsen, K.G., Srba, J.: Introducing modal transition systems with weight intervals (submitted)

    Google Scholar 

  17. Bruns, G., Godefroid, P.: Generalized model checking: Reasoning about partial state spaces. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 168–182. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  18. Godefroid, P., Piterman, N.: LTL generalized model checking revisited. In: Jones, N.D., Müller-Olm, M. (eds.) VMCAI 2009. LNCS, vol. 5403, pp. 89–104. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  19. Uchitel, S., Brunet, G., Chechik, M.: Synthesis of partial behavior models from properties and scenarios. IEEE Trans. Software Eng. 35(3), 384–406 (2009)

    Article  Google Scholar 

  20. D’Ippolito, N., Fischbein, D., Chechik, M., Uchitel, S.: MTSA: The modal transition system analyser. In: Proc. of ASE 2008, pp. 475–476. IEEE, Los Alamitos (2008)

    Google Scholar 

  21. Beneš, N., Černá, I., Křetínský, J.: Disjunctive modal transition systems and generalized LTL model checking. Technical report FIMU-RS-2010-12, Faculty of Informatics, Masaryk University, Brno (2010)

    Google Scholar 

  22. Beneš, N., Křetínský, J.: Process algebra for modal transition systemses. In: MEMICS. OASICS, vol. 16, pp. 9–18. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany (2010)

    Google Scholar 

  23. Beneš, N., Křetínský, J., Larsen, K.G., Srba, J.: Checking thorough refinement on modal transition systems is EXPTIME-complete. In: Leucker, M., Morgan, C. (eds.) ICTAC 2009. LNCS, vol. 5684, pp. 112–126. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  24. Pnueli, A.: The temporal logic of programs. In: FOCS, pp. 46–57. IEEE, Los Alamitos (1977)

    Google Scholar 

  25. Chaki, S., Clarke, E.M., Ouaknine, J., Sharygina, N., Sinha, N.: State/event-based software model checking. In: Boiten, E.A., Derrick, J., Smith, G.P. (eds.) IFM 2004. LNCS, vol. 2999, pp. 128–147. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  26. Godefroid, P., Jagadeesan, R.: Automatic abstraction using generalized model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 137–151. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  27. Godefroid, P., Jagadeesan, R.: On the expressiveness of 3-valued models. In: Zuck, L.D., Attie, P.C., Cortesi, A., Mukhopadhyay, S. (eds.) VMCAI 2003. LNCS, vol. 2575, pp. 206–222. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  28. Pnueli, A., Rosner, R.: On the synthesis of an asynchronous reactive module. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372, pp. 652–671. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  29. Dams, D., Namjoshi, K.S.: Automata as abstractions. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 216–232. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  30. Alur, R., Torre, S.L.: Deterministic generators and games for LTL fragments. ACM Trans. Comput. Log. 5(1), 1–25 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  31. Piterman, N., Pnueli, A.: Faster solution of rabin and streett games. In: Proceedings of LICS 2006, pp. 275–284. IEEE press, Los Alamitos (2006)

    Google Scholar 

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

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Informatics, Masaryk University, Brno, Czech Republic

    Nikola Beneš, Ivana Černá & Jan Křetínský

  2. Institut für Informatik, Technische Universität München, Germany

    Jan Křetínský

Authors
  1. Nikola Beneš
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ivana Černá
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jan Křetínský
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of California, Santa Barbara, CA, USA

    Tevfik Bultan

  2. Department of Computer Science and Information Engineering, National Chung Cheng University, 168 University Road, Min-Hsiung, 62102, Chiayi, Taiwan, ROC

    Pao-Ann Hsiung

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Beneš, N., Černá, I., Křetínský, J. (2011). Modal Transition Systems: Composition and LTL Model Checking. In: Bultan, T., Hsiung, PA. (eds) Automated Technology for Verification and Analysis. ATVA 2011. Lecture Notes in Computer Science, vol 6996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24372-1_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24372-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24371-4

  • Online ISBN: 978-3-642-24372-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation