An instantiation scheme for satisfiability modulo theories

Journal of Automated Reasoning

Volumn 48, Issue 3, 2012, Pages 293-362

  Echenim, Mnacho ^a   Peltier, Nicolas ^a  

^a UNIV GRENOBLE ALPES   (France)

Author keywords

Decision procedures; Instantiation based theorem proving; Satisfiability modulo theories

Indexed keywords

SYNTACTICS; THEOREM PROVING;

DECISION PROCEDURE; SATISFIABILITY MODULO THEORIES; SYNTACTIC CRITERIA; THEORY SOLVERS;

FORMAL LOGIC;

EID: 84881395968     PISSN: 01687433     EISSN: 15730670     Source Type: Journal    
DOI: 10.1007/s10817-010-9200-3     Document Type: Article

References (37)

1. Abadi, A., Rabinovich, A., Sagiv, M.: Decidable fragments of many-sorted logic. J. Symb. Comput. 45(2), 153-172 (2010)
2. Armando, A., Bonacina, M.P., Ranise, S., Schulz, S.: New results on rewrite-based satisfiability procedures. ACM Trans. Comput. Log. 10(1), 129-179 (2009)
3. Armando, A., Ranise, S., Rusinowitch,M.: A rewriting approach to satisfiability procedures. Inf. Comput. 183(2), 140-164 (2003)
4. Baader, F., Snyder, W.: Unification theory. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, chapter 8, pp. 445-532. Elsevier Science (2001)
5. Bachmair, L., Ganzinger, H.: Rewrite-based equational theorem proving with selection and simplification. J. Log. Comput. 3(4), 217-247 (1994)
6. Barrett, C., Sebastiani, R., Seshia, S., Tinelli, C.: Satisfiability modulo theories. In: Biere, A., Heule,M.J.H., van Maaren,H., Walsh, T. (eds.) Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185, chapter 26, pp. 825-885. IOS Press (2009)
7. Barrett, C.W.,Dill, D.L., Stump,A.: Checking satisfiability of first-order formulas by incremental translation to sat. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 236-249. Springer (2002)
8. Bofill, M., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E., Rubio, A.: A write-based solver for sat modulo the theory of arrays. In: FMCAD '08: Proceedings of the 2008 International Conference on Formal Methods in Computer-Aided Design, pp. 1-8. IEEE Press, Piscataway, NJ, USA (2008)
9. Bonacina, M.P., Echenim, M.: On variable-inactivity and polynomial T-satisfiability procedures. J. Log. Comput. 18(1), 77-96 (2008)
10. Bonacina, M.P., Echenim, M.: Theory decision by decomposition. J. Symb. Comput. 45(2), 229-260 (2010)
11. Bonacina,M.P., Ghilardi, S., Nicolini, E., Ranise, S., Zucchelli, D.: Decidability and undecidability results for Nelson-Oppen and rewrite-based decision procedures. In: Furbach, U., Shankar, N. (eds.) Proc. IJCAR-3. LNAI, vol. 4130, pp. 513-527. Springer (2006)
12. Bradley, A.R.,Manna, Z.: The Calculus of Computation: Decision Procedures with Applications to Verification. Springer-Verlag New York, Inc., Secaucus, NJ, USA (2007)
13. Bradley, A.R., Manna, Z., Sipma, H.B.: What's decidable about arrays? In: Emerson, E.A., Namjoshi, K.S. (eds.) Proc. VMCAI-7. LNCS, vol. 3855, pp. 427-442. Springer (2006)
14. Dantzig, G.B., Eaves, B.C.: Fourier-motzkin elimination and its dual. J. Comb. Theory, Ser. A 14(3), 288-297 (1973)
15. Davis, M., Logemann, G., Loveland, D.: A machine program for theorem proving. Commun. ACM 5, 394-397 (1962)
16. Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7(3), 201-215 (1960)
17. de Moura, L., Bjørner, N.: Engineering DPLL(T) + saturation. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR-4. LNAI, vol. 5195, pp. 475-490. Springer (2008)
18. de Moura, L., Bjørner, N.: Efficient e-matching for SMT solvers. In: Pfenning, F. (ed.) CADE-21. LNCS, vol. 4603, pp. 183-198. Springer (2007)
19. de Moura, L.M., Bjørner, N.: Generalized, efficient array decision procedures. In: FMCAD, pp. 45-52. IEEE (2009)
20. de Moura, L.M., Bjørner, N.: Efficient e-matching for SMT solvers. In: Pfenning, F. (ed.) 21st International Conference on Automated Deduction. LNCS, vol. 4603, pp. 183-198. Springer (2007)
21. Detlefs, D.L., Nelson, G., Saxe, J.B.: Simplify: a theorem prover for program checking. J. ACM 52(3), 365-473 (2005)
22. Dutertre, D., de Moura, L.: The YICES SMT-solver. In: SMT-COMP: satisfiability modulo theories competition. Available at http://yices.csl.sri. com (2006)
23. Echenim, M., Peltier, N.: Instantiation of SMT problems modulo integers. In: AISC 2010 (10th International Conference on Artificial Intelligence and Symbolic Computation). LNCS. Springer (2010)
24. Ganzinger, H., Korovin, K.: Integrating equational reasoning into instantiation-based theorem proving. In: Computer Science Logic (CSL'04), LNCS, vol. 3210, pp. 71-84. Springer (2004)
25. Ge, Y., Barrett, C.W., Tinelli, C.: Solving quantified verification conditions using satisfiability modulo theories. Ann. Math. Artif. Intell. 55(1-2), 101-122 (2009)
26. Ge, Y., de Moura, L.M.: Complete instantiation for quantified formulas in satisfiabiliby modulo theories. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 306-320. Springer (2009)
27. Goel, A., Krstíc, S., Fuchs, A.: Deciding array formulas with frugal axiom instantiation. In: SMT '08/BPR '08: Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning, pp. 12-17. ACM, New York, NY, USA (2008)
28. Jacobs, S.: Incremental instance generation in local reasoning. In: Baader, F., Ghilardi, S., Hermann, M., Sattler, U., Sofronie-Stokkermans, V. (eds.) Notes 1st CEDAR Workshop, IJCAR 2008, pp. 47-62 (2008)
29. Jouannaud, J., Kirchner, C.: Solving equations in abstract algebras: a rule based survey of unification. In: Lassez, J.-L., Plotkin, G. (eds.) Essays in Honor of Alan Robinson, pp. 91-99. MIT Press (1991)
30. Kirchner, C., Kirchner, H., Rusinowitch, M.: Deduction with symbolic constraints. Revue Française d'Intelligence Artificielle 4(3), 9-52 (1990)
31. Kirchner, H., Ranise, S., Ringeissen, C., Tran, D.-K.: Automatic combinability of rewriting-based satisfiability procedures. In: Hermann, M., Voronkov,A. (eds.) Proc. LPAR-13. LNCS, vol. 4246, pp. 542-556. Springer (2006)
32. Lee, S., Plaisted, D.A.: Eliminating duplication with the hyper-linking strategy. J. Autom. Reason. 9, 25-42 (1992)
33. Lynch, C., Tran, D.-K.: Automatic decidability and combinability revisited. In: Pfenning, F. (ed.) CADE-21. LNAI, vol. 4603, pp. 328-344. Springer (2007)
34. Plaisted, D.A., Zhu, Y.:Ordered semantic hyperlinking. J.Autom. Reason. 25(3), 167-217 (2000)
35. Ranise, S., Deharbe, D.: Applying light-weight theorem proving to debugging and verifying pointer programs. In: Proc. of the 4th Workshop on First-order Theorem Proving (FTP'03). Electronic Notes in Theoretical Computer Science, vol. 86 (2003)
36. Stump, A., Barrett, C.W., Dill, D.L., Levitt, J.: A decision procedure for an extensional theory of arrays. In: LICS '01: Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science, p. 29. IEEE Computer Society, Washington, DC, USA (2001)
37. Waldmann, U., Prevosto, V.: SPASS+T. In: Sutcliffe, G., Schmidt, R., Schulz, S. (eds.) Proc. ESCoR Workshop, FLoc 2006. CEUR Workshop Proceedings, vol. 192, pp. 18-33 (2006)