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.
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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)
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)
Bjorner, N.: Integrating Decision Procedures for Temporal Verification. PhD thesis. Stanford University (1999)
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)
Cyrluk, D.: Private communication (1999)
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)
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)
Detlefs, D.L., Rustan, K., Leino, M., Nelson, G., Saxe, J.B.: Extended static checking. Technical Report 159, Compaq SRC (1998)
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)
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)
Levitt, J.: Formal Verification Techniques for Digital Systems. PhD thesis. Stanford University (1999)
Nelson, G., Oppen, D.: Simplification by cooperating decision procedures. ACM Transactions on Programming Languages and Systems 1(2), 245–257 (1979)
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)
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)
Pugh, W.: The omega test: a fast and practical integer programming algorithm for dependence analysis. Communications of the ACM 8, 102–114 (1992)
Ruess, H., Shankar, N.: Deconstructing Shostak. In: 17th International Conference on Computer Aided Deduction (2000)
Shostak, R.: Deciding combinations of theories. Journal of the Association for Computing Machinery 31(1), 1–12 (1984)
Su, J., Dill, D., Skakkebæk, J.: Formally verifying data and control with weak reachability invariants. Formal Method In Computer-Aided Design (1998)
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)
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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
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DOI: https://doi.org/10.1007/10721959_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67664-5
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