A tutorial on satisfiability modulo theories

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4590 LNCS, Issue , 2007, Pages 20-36

  De Moura, Leonardo ^a   Dutertre, Bruno ^b   Shankar, Natarajan ^b  

^a MICROSOFT RESEARCH   (United States)

^b SRI INTERNATIONAL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN FUNCTIONS; CONSTRAINT THEORY; SECURITY OF DATA; SOFTWARE TESTING; VERIFICATION;

SATISFIABILITY MODULO THEORIES; SATISFIABILITY SOLVERS; TEST CASE GENERATION;

PROBLEM SOLVING;

EID: 38149058155     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-73368-3_5     Document Type: Conference Paper

References (36)

1. 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, Springer, Heidelberg (2002)
2. Bachmair, L., Tiwari, A., Vigneron, L.: Abstract congruence closure. Journal of Automated Reasoning 31(2), 129-168 (2003)
3. Cherkassky, B.V., Goldberg, A.V: Negative-cycle detection algorithms. In: European Symposium on Algorithms, pp. 349-363 (1996)
4. Craig, W: Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory. Journal of Symbolic Logic 22(3), 269-285 (1957)
5. Dutertre, B., de Moura, L.: A fast linear-arithmetic solver for dpll(t). In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 81-94. Springer, Heidelberg (2006)
6. Dutertre, B., de. Moura, L.: The Yices SMT solver (2006)
7. Davis, M., Logemann, G., Loveland, D.: A machine program for theorem proving. Communications of the ACM 5(7), 394-397 (1962)
8. Reprinted in Siekmann and WrightsonSiekmannWrightson83, pp. 267-270, (1983)
9. de Moura, L., Rue, H., Sorea, M.: Lazy theorem proving for bounded model checking over infinite domains. In: Voronkov, A. (ed.) Automated Deduction - CADE-18. LNCS (LNAI), vol. 2392, pp. 438-455. Springer, Heidelberg (2002)
10. de Moura, L., Rue\ss, H., Shankar, N.: Justifying equality. In: Proceedings of PDPAR '04 (2004)
11. Detlefs, D., Nelson, G., Saxe, J.B.: Simplify: A theorem prover for program checking. In: Technical Report HPL-2003-148, Hewlett-Packard Systems Research Center (2003)
12. Davis, M., Putnam, H. : A computing procedure for quantification theory. JACM 7(3), 201-215 (1960)
13. Eén, N., Sörensson, N.: An extensible SAT-solver. In: SAT 2003 (2003)
14. Flanagan, C., Joshi, R., Ou, X., Saxe, J.B.: Theorem proving using lazy proof explication. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 355-367. Springer, Heidelberg (2003)
15. Galler, B.A., Fisher, M.J.: An improved equivalence algorithm. Commun. ACM 7(5), 301-303 (1964)
16. Goldberg, E., Novikov, Y.: Berkmin: A fast and robust sat solver (2002)
17. Kozen, D.: Complexity of finitely presented algebras. In: Conference Record of the Ninth Annual ACM Symposium on Theory of Computing, pp. 164-177, Boulder, Colorado (May 2-4,1977)
18. McMillan, K.L.: An interpolating theorem prover. Theor. Comput. Sci. 345(1), 101-121 (2005)
19. Matthew, W., Moskewicz, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: Proceedings of the 38th Design Automation Conference (DAC'01) (June 2001)
20. Marques-Silva, J., Sakallah, K.: GRASP: A search algorithm for propositional satisfiability. IEEE Transactions on Computers 48(5), 506-521 (1999)
21. Nelson, G.: Techniques for program verification. Technical Report CSL-81-10, Xerox Palo Alto Research Center, Palo Alto, Ca (1981)
22. Nelson, G., Oppen, D.C.: Simplification by cooperating decision procedures. ACM Transactions on Programming Languages and Systems 1(2), 245-257 (1979)
23. Nieuwenhuis, R., Oliveras, A.: Robert Nieuwenhuis and Albert Oliveras. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 453-168. Springer, Heidelberg (2005)
24. Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT Modulo Theories: From an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). J. ACM 53(6), 937-977 (2006)
25. Derek, C.: Complexity, convexity and combinations of theories. Theoretical Computer Science 12, 291-302 (1980)
26. Ryan, L.: Efficient algorithms for clause-learning SAT solvers. Master's thesis, Simon Fraser University, M.Sc. Thesis (2004)
27. Shankar, N.: Inference systems for logical algorithms. In: Ramanujam, R., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 60-78. Springer, Heidelberg (2005)
28. Shostak, R.: An algorithm for reasoning about equality. Comm. ACM 21, 583-585 (1978)
29. Shostak, R.: A practical decision procedure for arithmetic with function symbols. JACM 26(2), 351-360 (1979)
30. Selman, B., Kautz, H., Cohen, B.: Local search strategies for satisfiability testing. In: Johnson, D.S., Trick, M.A. (eds.) Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, vol. 26 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science. AMS (1996)
31. Siekmann, J., Wrightson, G. (eds.): Automation of Reasoning: Classical Papers on Computational Logic, vol. 1 & 2. Springer, Heidelberg (1983)
32. Tarjan, R.E.: Efficiency of a good but not linear set union algorithm. J. ACM 22(2), 215-225 (1975)
33. Wang, C., Ivančić, F., Ganai, M., Gupta, A.: Deciding separation logic formulae by SAT and incremental negative cycle elimination. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS (LNAI), vol. 3835, pp. 322-336. Springer, Heidelberg (2005)
34. Zhang, H.: SATO: An efficient propositional prover. In: Conference on Automated Deduction, pp. 272-275 (1997)
35. Zhang, L.: Searching for Truth: Techniques for Satisfiability of Boolean Formulas. PhD thesis, Princeton University (2003)
36. Zhang, L., Malik, S.: The quest for efficient boolean satisfiability solvers. In: Voronkov, A. (ed.) Proceedings of CADE-19, Berlin, Germany, Springer, Heidelberg (2002)