Skip to main content

A Framework for Cooperating Decision Procedures

  • Conference paper
Automated Deduction - CADE-17 (CADE 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1831))

Included in the following conference series:

Abstract

We present a flexible framework for cooperating decision procedures. We describe the properties needed to ensure correctness and show how it can be applied to implement an efficient version of Nelson and Oppen’s algorithm for combining decision procedures. We also show how a Shostak style decision procedure can be implemented in the framework in such a way that it can be integrated with the Nelson–Oppen method.

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

Access this chapter

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. Baader, F., Tinelli, C.: A new approach for combining decision procedures for the word problem, and its connection to the Nelson–Oppen combination method. In: McCune, W. (ed.) 14th International Conference on Computer Aided Deduction. LNCS, pp. 19–33. Springer, Heidelberg (1997)

    Google Scholar 

  2. Barrett, C., Dill, D., Levitt, J.: Validity checking for combinations of theories with equality. In: Srivas, M., Camilleri, A. (eds.) FMCAD 1996. LNCS, vol. 1166, pp. 187–201. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  3. Bjorner, N.: Integrating Decision Procedures for Temporal Verification. PhD thesis. Stanford University (1999)

    Google Scholar 

  4. Colon, M.A., Uribe, T.E.: Generating finite-state abstractions of reactive systems using decision procedures. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 293–304. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  5. Cyrluk, D.: Private communication (1999)

    Google Scholar 

  6. Cyrluk, D., Lincoln, P., Shankar, N.: On Shostak’s Decision Procedure for Com- binations of Theories. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS, vol. 1104, pp. 463–477. Springer, Heidelberg (1996)

    Google Scholar 

  7. Das, S., Dill, D.L., Park, S.: Experience with predicate abstraction. In: 11th International Conference on Computer-Aided Verification, Trento, Italy, pp. 160–172. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  8. Detlefs, D.L., Rustan, K., Leino, M., Nelson, G., Saxe, J.B.: Extended static checking. Technical Report 159, Compaq SRC (1998)

    Google Scholar 

  9. Manna, Z., et al.: STeP: Deductive-Algorithmic Verification of Reactive and Real- time Systems. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 415–418. Springer, Heidelberg (1996)

    Google Scholar 

  10. Saidi, H., Shankar, N.: Abstract and model check while you prove. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 443–454. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  11. Levitt, J.: Formal Verification Techniques for Digital Systems. PhD thesis. Stanford University (1999)

    Google Scholar 

  12. Nelson, G., Oppen, D.: Simplification by cooperating decision procedures. ACM Transactions on Programming Languages and Systems 1(2), 245–257 (1979)

    Article  MATH  Google Scholar 

  13. Owre, S., Rushby, J., Shankar, N.: PVS: A Prototype Verification System. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 748–752. Springer, Heidelberg (1992)

    Google Scholar 

  14. Park, D.Y.W., Skakkebæk, J.U., Heimdahl, M.P.E., Czerny, B.J., Dill, D.L.: Checking properties of safety critical specifications using efficient decision procedures. In: FMSP 1998: Second Workshop on Formal Methods in Software Practice, March 1998, pp. 34–43 (1998)

    Google Scholar 

  15. Pugh, W.: The omega test: a fast and practical integer programming algorithm for dependence analysis. Communications of the ACM 8, 102–114 (1992)

    Article  Google Scholar 

  16. Ruess, H., Shankar, N.: Deconstructing Shostak. In: 17th International Conference on Computer Aided Deduction (2000)

    Google Scholar 

  17. Shostak, R.: Deciding combinations of theories. Journal of the Association for Computing Machinery 31(1), 1–12 (1984)

    MATH  MathSciNet  Google Scholar 

  18. Su, J., Dill, D., Skakkebæk, J.: Formally verifying data and control with weak reachability invariants. Formal Method In Computer-Aided Design (1998)

    Google Scholar 

  19. Tinelli, C., Harandi, M.: A new Correctness Proof of the Nelson–Oppen Combination Procedure. In: Baader, F., Schulz, K. (eds.) 1st International Workshop on Frontiers of Combining Systems (FroCoS’96). Applied Logic Series, vol. 3. Kluwer Academic Publishers, Dordrecht (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Barrett, C.W., Dill, D.L., Stump, A. (2000). A Framework for Cooperating Decision Procedures. In: McAllester, D. (eds) Automated Deduction - CADE-17. CADE 2000. Lecture Notes in Computer Science(), vol 1831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10721959_6

Download citation

  • DOI: https://doi.org/10.1007/10721959_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67664-5

  • Online ISBN: 978-3-540-45101-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics