Skip to main content
SpringerLink
Log in

Automated Compositional Reasoning of Intuitionistically Closed Regular Properties

  • Conference paper
Implementation and Applications of Automata (CIAA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5148))

Included in the following conference series:

  • 454 Accesses

Abstract

Analysis of infinitary safety properties with automated compositional reasoning through learning is discussed. We consider the class of intuitionistically closed regular languages and show that it forms a Heyting algebra and is finitely approximatable. Consequently, compositional proof rules can be verified automatically and learning algorithms for finitary regular languages suffice for generating the needed contextual assumptions. We also provide a semantic justification of an axiom to deduce circular compositional proof rules for such infinitary languages.

The work is partly supported by NSC grant 96-3114-P-001-002-Y. The second author is also supported by NSC grant 95-2221-E-001-024-MY3 and the SISARL thematic project of Academia Sinica.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abadi, M., Plotkin, G.D.: A logical view of composition. Theoretical Computer Science 114(1), 3–30 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alpern, B., Schneider, F.: Defining liveness. Information Processing Letters 21, 181–185 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  3. Alur, R., Henzinger, T.: Reactive modules. Formal Methods in System Design 15(1), 7–48 (1999)

    Article  MathSciNet  Google Scholar 

  4. Angluin, D.: Learning regular sets from queries and counterexamples. Information and Computation 75(2), 87–106 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  5. Barringer, H., Giannakopoulou, D., Pǎsǎreanu, C.S.: Proof rules for automated compositional verification through learning. In: Workshop on Specification and Verification of Component-Based Systems, pp. 14–21 (2003)

    Google Scholar 

  6. Cobleigh, J.M., Giannakopoulou, D.: Learning assumptions for compositional verification. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 331–346. Springer, Heidelberg (2003)

    Google Scholar 

  7. de Roever, W.P., de Boer, F., Hanneman, U., Hooman, J., Lakhnech, Y., Poel, M., Zwiers, J.: Concurrency Verification: Introduction to Compositional and Noncompositional Methods. Cambridge Tracts in Theoretical Computer Science, vol. 54. Cambridge University Press, Cambridge (2001)

    MATH  Google Scholar 

  8. Farzan, A., Chen, Y.F., Clarke, E.M., Tsay, Y.K., Wang, B.Y.: Extending automated compositional verification to the full class of omega-regular languages. In: Ramakrishnan, C., Rehof, J. (eds.) TACAS. LNCS, vol. 4963, pp. 2–17. Springer, Heidelberg (2008)

    Google Scholar 

  9. Goldblatt, R.: Topoi: The Categorial Analysis of Logic, revised edn. Dover Publications (2006)

    Google Scholar 

  10. Landweber, L.: Decision problems for ω-automata. Mathematical Systems Theory 3, 376–384 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  11. Maier, P.: Intuitionistic LTL and a new characterization of safety and liveness. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 295–309. Springer, Heidelberg (2004)

    Google Scholar 

  12. Maler, O., Pnueli, A.: On the learnability of infinitary regular sets. Information and Computation 118(2), 316–326 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  13. Rivest, R.L., Schapire, R.E.: Inference of finite automata using homing sequences. Information and Computation 103(2), 299–347 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  14. Staiger, L.: ω-languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 339–387. Springer, Heidelberg (1997)

    Google Scholar 

  15. Thomas, W.: Automata on infinite objects. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 133–191. Elsevier Science Publishers, Amsterdam (1990)

    Google Scholar 

  16. Vardi, M.: Verification of concurrent programs: the automata-theoretic framework. In: Proceedings of the Second IEEE Symposium on Logic in Computer Science, pp. 167–176 (1987)

    Google Scholar 

  17. Wagner, K.: On ω-regular sets. Information and Control 43, 123–177 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  18. Wang, B.Y.: Automatic derivation of compositional rules in automated compositional reasoning. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR. LNCS, vol. 4703, pp. 303–316. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Management, National Taiwan University, Taiwan

    Yih-Kuen Tsay

  2. Institute of Information Science, Academia Sinica,  , Taiwan

    Bow-Yaw Wang

Authors
  1. Yih-Kuen Tsay
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bow-Yaw Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Oscar H. Ibarra Bala Ravikumar

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tsay, YK., Wang, BY. (2008). Automated Compositional Reasoning of Intuitionistically Closed Regular Properties. In: Ibarra, O.H., Ravikumar, B. (eds) Implementation and Applications of Automata. CIAA 2008. Lecture Notes in Computer Science, vol 5148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70844-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-70844-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70843-8

  • Online ISBN: 978-3-540-70844-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation