Satisfiability modulo theories

Frontiers in Artificial Intelligence and Applications

Volumn 185, Issue 1, 2009, Pages 825-885

  Barrett, Clark ^a   Sebastiani, Roberto ^a   Seshia, Sanjit A ^a   Tinelli, Cesare ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

FORMAL LOGIC; FORMAL VERIFICATION;

BACKGROUND THEORY; BITVECTORS; DECISION PROCEDURE; FINITE SIZE; FIRST ORDER; FIRST ORDER LOGIC; FUNCTION SYMBOLS; SATISFIABILITY; SATISFIABILITY MODULO THEORIES; THEORY SOLVERS;

DECISION THEORY;

EID: 69949133234     PISSN: 09226389     EISSN: 18798314     Source Type: Book Series    
DOI: 10.3233/978-1-58603-929-5-825     Document Type: Article

References (162)

1. G. Audemard, P. Bertoli, A. Cimatti, A. Korni lowicz, and R. Sebastiani. A SAT Based Approach for Solving Formulas over Boolean and Linear Mathematical Propositions. In Proc. CADE'2002., volume 2392 of LNAI. Springer, July 2002.
2. A. Armando, M. P. Bonacina, S. Ranise, and S. Schulz. On a rewriting approach to satisfiability procedures: Extension, combination of theories and an experimental appraisal. In B. Gramlich, editor, Frontiers of Combining Systems, 5th International Workshop, FroCoS 2005, Vienna, Austria, September 19-21, 2005, Proceedings, volume 3717 of Lecture Notes in Computer Science, pages 65-80. Springer, 2005.
3. A. Armando, C. Castellini, and E. Giunchiglia. SAT-based procedures for temporal reasoning. In Proc. European Conference on Planning, ECP-99, 1999.
4. A. Armando, C. Castellini, E. Giunchiglia, and M. Maratea. A SATbased Decision Procedure for the Boolean Combination of Difference Constraints. In Proc. SAT'04, 2004.
5. W. Ackermann. Solvable Cases of the Decision Problem. North- Holland, Amsterdam, 1954.
6. G. Audemard, A. Cimatti, A. Korni lowicz, and R. Sebastiani. SATBased Bounded Model Checking for Timed Systems. In Proc. FORTE'02., volume 2529 of LNCS. Springer, November 2002.
7. A. Armando and E. Giunchiglia. Embedding Complex Decision Procedures inside an Interactive Theorem Prover. Annals of Mathematics and Artificial Intelligence, 8(3-4):475-502, 1993.
8. H. Amjad. A Compressing Translation from Propositional Resolution to Natural Deduction. In Proc. FroCoS, volume 4720 of Lecture Notes in Computer Science, pages 88-102. Springer, 2007.
9. A. Armando, S. Ranise, and M. Rusinowitch. A Rewriting Approach to Satisfiability Procedures. Information and Computation, 183(2):140-164, June 2003.
10. C. Barrett and S. Berezin. A proof-producing boolean search engine. In Proceedings of the 1st International Workshop on Pragmatics of Decision Procedures in Automated Reasoning (PDPAR '03), July 2003.
11. C. Barrett and S. Berezin. CVC Lite: A new implementation of the cooperating validity checker. In R. Alur and D. A. Peled, editors, Proceedings of the 16th International Conference on Computer Aided Verification (CAV '04), volume 3114 of Lecture Notes in Computer Science, pages 515-518. Springer, July 2004.
12. M. Bozzano, R. Bruttomesso, A. Cimatti, T. Junttila, P. Rossum, S. Schulz, and R. Sebastiani. An incremental and Layered Procedure for the Satisfiability of Linear Arithmetic Logic. In Proc. TACAS'05, volume 3440 of LNCS. Springer, 2005.
13. M. Bozzano, R. Bruttomesso, A. Cimatti, T. Junttila, P. Rossum, S. Schulz, and R. Sebastiani. MathSAT: A Tight Integration of SAT and Mathematical Decision Procedure. Journal of Automated Reasoning, 35(1-3), October 2005.
14. M. Bozzano, R. Bruttomesso, A. Cimatti, T. Junttila, P. van Rossum, S. Ranise, and R. Sebastiani. Efficient Satisfiability Modulo Theories via Delayed Theory Combination. In Proc. CAV 2005, volume 3576 of LNCS. Springer, 2005.
15. M. Bozzano, R. Bruttomesso, A. Cimatti, T. Junttila, P. van Rossum, S. Ranise, and R. Sebastiani. Efficient Theory Combination via Boolean Search. Information and Computation, 204(10), 2006.
16. R. Bruttomesso, A. Cimatti, A. Franźen, A. Griggio, A. Santuari, and R. Sebastiani. To Ackermann-ize or not to Ackermannize? On Efficiently Handling Uninterpreted Function Symbols in SMT(EUF?T ). In Proc. LPAR'06, volume 4246 of LNAI. Springer, 2006.
17. R. Bruttomesso, A. Cimatti, A. Franźen, A. Griggio, and R. Sebastiani. Delayed Theory Combination vs. Nelson-Oppen for Satisfiability Modulo Theories: a Comparative Analysis. In Proc. LPAR'06, volume 4246 of LNAI. Springer, 2006.
18. R. Bruttomesso, A. Cimatti, A. Franźen, A. Griggio, Z. Hanna, A. Nadel, A. Palti, and R. Sebastiani. A lazy and layered SMT(BV) solver for hard industrial verification problems. In W. Damm and H. Hermanns, editors, Proceedings of the 19th International Conference on Computer Aided Verification (CAV '07), volume 4590 of Lecture Notes in Computer Science, pages 547-560. Springer-Verlag, July 2007.
19. T. Ball, B. Cook, S. Lahiri, and L. Zhang. Zapato: Automatic theo rem proving for predicate abstraction refinement. In Proc. Computer- Aided Verification (CAV), volume 3114 of Lecture Notes in Computer Science, pages 457-461, 2004.
20. C. W. Barrett, D. L. Dill, and J. R. Levitt. A decision procedure for bit-vector arithmetic. In Proceedings of the 35th Design Automation Conference (DAC '98), pages 522-527. Association for Computing Machinery, June 1998.
21. N. Bjorner and L. de Moura. Efficient E-matching for SMT solvers. In F. Pfenning, editor, Proceedings of the 21st International Conference on Automated Deduction (CADE '07), volume 4603 of Lecture Notes in Artificial Intelligence, pages 183-198. Springer-Verlag, July 2007.
22. C. W. Barrett, D. L. Dill, and A. Stump. Checking satisfiability of first-order formulas by incremental translation to SAT. In E. Brinksma and K. G. Larsen, editors, Proceedings of the 14th International Conference on Computer Aided Verification (CAV '02), volume 2404 of Lecture Notes in Computer Science, pages 236-249. Springer-Verlag, July 2002.
23. C. W. Barrett, D. L. Dill, and A. Stump. A generalization of Shostak's method for combining decision procedures. In A. Armando, editor, Proceedings of the 4th International Workshop on Frontiers of Combining Systems (FroCoS '02), volume 2309 of Lecture Notes in Artificial Intelligence, pages 132-146. Springer, April 2002.
24. C. W. Barrett, D. L. Dill, and A. Stump. A generalization of Shostak's method for combining decision procedures. In A. Armando, editor, Proceedings of the 4th International Workshop on Frontiers of Combining Systems, FroCoS'2002 (Santa Margherita Ligure, Italy), volume 2309 of Lecture Notes in Computer Science, pages 132-147, apr 2002.
25. M. P. Bonacina and M. Echenim. Rewrite-based decision procedures. In M. Archer, T. B. de la Tour, and C. Munoz, editors, Proceedings of the Sixth Workshop on Strategies in Automated Deduction (STRATEGIES), volume 174(11) of Electronic Notes in Theoretical Computer Science, pages 27-45. Elsevier, July 2007.
26. M. P. Bonacina and M. Echenim. T-decision by decomposition. In F. Pfenning, editor, Proceedings of the Twenty-first International Conference on Automated Deduction (CADE), volume 4603 of Lecture Notes in Artificial Intelligence, pages 199-214. Springer, July 2007.
27. I. Borosh, M. Flahive, and L. B. Treybig. Small solutions of linear Diophantine equations. Discrete Mathematics, 58:215-220, 1986.
28. M. P. Bonacina, S. Ghilardi, E. Nicolini, S. Ranise, and D. Zucchelli. Decidability and undecidability results for Nelson-Oppen and rewrite-based decision procedures. In U. Furbach and N. Shankar, editors, Automated Reasoning, Third International Joint Conference, IJCAR 2006, Seattle, WA, USA, August 17-20, 2006, Proceedings, volume 4130 of Lecture Notes in Computer Science, pages 513-527. Springer, 2006.
29. M. P. Bonacina, S. Ghilardi, E. Nicolini, S. Ranise, and D. Zucchelli. Decidability and undecidability results for Nelson-Oppen and rewrite-based decision procedures. In U. Furbach and N. Shankar, editors, Proceedings of the 3rd International Joint Conference on Auto mated Reasoning (IJCAR 2006), volume 4130 of Lecture Notes in Computer Science, pages 513-527, Seattle (WA, USA), 2006. Springer.
30. R. E. Bryant, S. German, and M. N. Velev. Exploiting Positive Equality in a Logic of Equality with Uninterpreted Functions. In Proc. CAV'99, volume 1633 of LNCS. Springer, 1999.
31. R. E. Bryant, S. German, and M. N. Velev. Processor verification using efficient reductions of the logic of uninterpreted functions to propositional logic. ACM Transactions on Computational Logic, 2(1):1-41, January 2001.
32. R. E. Bryant, D. Kroening, J. Ouaknine, S. A. Seshia, O. Strichman, and B. Brady. Deciding bit-vector arithmetic with abstraction. In Proceedings of Tools and Algorithms for the Construction and Analysis of Systems (TACAS), volume 4424 of Lecture Notes in Computer Science, pages 358-372. Springer, 2007.
33. R. S. Boyer and J. Moore. Integrating decision procedures into heuristic theorem provers: A case study of linear arithmetic. Machine Intelligence, 11:83-124, 1988.
34. R. S. Boyer and J. S. Moore. A theorem prover for a computational logic. In M. E. Stickel, editor, 10th International Conference on Automated Deduction (CADE), LNAI 449, pages 1-15, Kaiserslautern, FRG, July 24-27, 1990. Springer-Verlag.
35. A. R. Bradley, Z. Manna, and H. B. Sipma. What's decidable about arrays? In Proc. Verification, Model-Checking, and Abstract- Interpretation (VMCAI), volume 3855 of LNCS, pages 427-442. Springer-Verlag, January 2006.
36. C. Barrett, R. Nieuwenhuis, A. Oliveras, and C. Tinelli. Splitting on demand in SAT modulo theories. In M. Hermann and A. Voronkov, editors, Proceedings of the 13th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR '06), volume 4246 of Lecture Notes in Computer Science, pages 512-526. Springer, November 2006. (Pubitemid 44850698)
37. C. Barrett, R. Nieuwenhuis, A. Oliveras, and C. Tinelli. Splitting on demand in SAT Modulo Theories. Technical Report 06-105, Department of Computer Science, University of Iowa, August 2006.
38. Booleforce, http://fmv.jku.at/booleforce/.
39. N. Bjorner and M. C. Pichora. Deciding fixed and non-fixed size bit-vectors. In TACAS '98: Proceedings of the 4th International Conference on Tools and Algorithms for Construction and Analysis of Systems, pages 376-392. Springer-Verlag, 1998.
40. C. Barrett, S. Ranise, C. Tinelli, and A. Stump. The SMT-LIB web site, 2008.
41. C. Barrett, I. Shikanian, and C. Tinelli. An abstract decision proce dure for a theory of inductive data types. Journal on Satisfiability, Boolean Modeling and Computation, 3:21-46, 2007.
42. I. Borosh and L. B. Treybig. Bounds on positive integral solutions of linear Diophantine equations. Proceedings of the American Mathematical Society, 55(2):299-304, March 1976.
43. C. Barrett and C. Tinelli. CVC3. In W. Damm and H. Hermanns, editors, Proceedings of the 19th International Conference on Computer Aided Verification (CAV '07), volume 4590 of Lecture Notes in Computer Science, pages 298-302. Springer, July 2007.
44. L. Bachmair, A. Tiwari, and L. Vigneron. Abstract congruence closure. Journal of Automated Reasoning, 31(2):129-168, 2003.
45. R. E. Bryant and M. N. Velev. Boolean satisfiability with transitivity constraints. In A. Emerson and P. Sistla, editors, Computer-Aided Verification (CAV 2000), LNCS 1855. Springer-Verlag, July 2000.
46. A. Cimatti, A. Griggio, and R. Sebastiani. A Simple and Flexible Way of Computing Small Unsatisfiable Cores in SAT Modulo Theories. In Proc. SAT'07, volume 4501 of LNCS. Springer, 2007.
47. A. Cimatti, A. Griggio, and R. Sebastiani. Efficient Interpolant Generation in Satisfiability Modulo Theories. In Proc. TACAS'08, volume 4963 of LNCS. Springer, 2008.
48. V. Chandru. Variable elimination in linear constraints. The Computer Journal, 36(5):463-472, August 1993.
49. S. Conchon and S. Krstíc. Strategies for combining decision procedures. Theoretical Computer Science, 354, 2006.
50. D. Cyrluk, P. Lincoln, and N. Shankar. On Shostak's decision procedure for combinations of theories. In M. McRobbie and J. Slaney, editors, 13th International Conference on Computer Aided Deduction, volume 1104 of Lecture Notes in Computer Science, pages 463-477. Springer, 1996.
51. S. Cotton and O. Maler. Fast and Flexible Difference Logic Propagation for DPLL(T). In Proc. SAT'06, volume 4121 of LNCS. Springer, 2006.
52. S. Cotton and O. Maler. Satisfiability modulo theory chains with DPLL(T). Unpublished. Available from http://www-verimag.imag.fr/?maler/, 2006.
53. D. Cyrluk, M. O. Möller, and H. Ruess. An efficient decision procedure for the theory of fixed-size bit-vectors. In Proceedings of the 9th International Conference on Computer Aided Verification (CAV '97), pages 60-71. Springer, 1997.
54. W. Craig. Linear reasoning: A new form of the Herbrand-Gentzen theorem. Journal of Symbolic Logic, 22(3):250-268, 1957.
55. B. Dutertre and L. de Moura. System Description: Yices 1.0. Proc. on 2nd SMT competition, SMT-COMP'06. Available at yices.csl.sri.com/yices-smtcomp06. pdf, 2006.
56. B. Dutertre and L. de Moura. A fast linear-arithmetic solver for DPLL(T). In T. Ball and R. B. Jones, editors, Proceedings of the 18th International Conference on Computer Aided Verification (CAV '06), volume 4144 of Lecture Notes in Computer Science, pages 81- 94. Springer, August 2006.
57. J. H. Davenport and J. Heintz. Real quantifier elimination is doubly exponential. Journal of Symbolic Computation, 5:29-35, 1988.
58. N. Dershowitz, Z. Hanna, and A. Nadel. A Scalable Algorithm for Minimal Unsatisfiable Core Extraction. In Proc. SAT'06, volume 4121 of LNCS. Springer, 2006.
59. L. de Moura and N. Bjorner. Model-based Theory Combination. In Proc. 5th workshop on Satisfiability Modulo Theories, SMT'07, 2007.
60. L. de Moura and N. Bjorner. Z3: An efficient SMT solver. In Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS '08), 2008.
61. L. de Moura, H. Rues, and M. Sorea. Lemmas on Demand for Satisfiability Solvers. Proc. SAT'02, 2002.
62. D. Detlefs, G. Nelson, and J. B. Saxe. Simplify: A theorem prover for program checking. Technical Report HPL-2003-2148, HP Laboratories Palo Alto, 2003.
63. P. J. Downey, R. Sethi, and R. E. Tarjan. Variations on the common subexpression problem. Journal of the Association for Computing Machinery, 27(4):758-771, October 1980.
64. H. D. Ebbinghaus, J. Flum, and W. Thomas. Mathematical logic. Undergraduate Texts in Mathematics. Springer, New York, second edition edition, 1994.
65. J. Elgaard, N. Klarlund, and A. Möller. Mona 1.x: New techniques for WS1S and WS2S. In Proceedings of the 10th International Conference on Computer Aided Verification (CAV '98), volume 1427 of Lecture Notes in Computer Science. Springer, 1998.
66. H. B. Enderton. A Mathematical Introduction to Logic. Undergraduate Texts in Mathematics. Academic Press, second edition edition, 2000.
67. P. Fontaine and E. P. Gribomont. Combining non-stably infinite, non-first order theories. In C. Tinelli and S. Ranise, editors, Proceedings of the IJCAR Workshop on Pragmatics of Decision Procedures in Automated Deduction, PDPAR, July 2004.
68. C. Flanagan, R. Joshi, X. Ou, and J. B. Saxe. Theorem Proving Using Lazy Proof Explication. In Proc. CAV 2003, LNCS. Springer, 2003.
69. J.-C. Filliâtre, S. Owre, H. Rues, and N. Shankar. ICS: integrated canonizer and solver. In Proceedings of the 13th International Conference on Computer Aided Verification (CAV'01), 2001.
70. P. Fontaine, S. Ranise, and C. G. Zarba. Combining lists with non-stably infinite theories. In F. Baader and A. Voronkov, editors, Logic for Programming, Artificial Intelligence, and Reasoning (LPAR), volume 3452 of Lecture Notes in Computer Science, pages 51-66. Springer-Verlag, 2005.
71. H. Ganzinger. Shostak light. In A. Voronkov, editor, Proceedings of the 18th International Conference on Computer-Aided Deduction CADE '02), volume 2392 of Lecture Notes in Artificial Intelligence, pages 332-346. Springer, July 2002.
72. Y. Ge, C. Barrett, and C. Tinelli. Solving quantified verification conditions using satisfiability modulo theories. In F. Pfenning, editor, Proceedings of the 21st International Conference on Automated Deduction (CADE '07), volume 4603 of Lecture Notes in Artificial Intelligence, pages 167-182. Springer-Verlag, July 2007.
73. V. Ganesh and D. L. Dill. A decision procedure for bit-vectors and arrays. In W. Damm and H. Hermanns, editors, Proceedings of the 19th International Conference on Computer Aided Verification (CAV '07), volume 4590 of Lecture Notes in Computer Science, pages 519- 531. Springer-Verlag, July 2007.
74. E. Giunchiglia, F. Giunchiglia, and A. Tacchella. SAT Based Decision Procedures for Classical Modal Logics. Journal of Automated Reasoning. Special Issue: Satisfiability at the start of the year 2000, 2001.
75. S. Ghilardi. Model theoretic methods in combined constraint satisfiability. Journal of Automated Reasoning, 3(3-4):221-249, 2004.
76. H. Ganzinger, G. Hagen, R. Nieuwenhuis, A. Oliveras, and C. Tinelli. DPLL(T): Fast Decision Procedures. In Proc. CAV'04, volume 3114 of LNCS. Springer, 2004.
77. R. Gershman, M. Koifman, and O. Strichman. Deriving Small Unsatisfiable Cores with Dominators. In Proc. CAV'06, volume 4144 of LNCS. Springer, 2006.
78. S. Ghilardi, E. Nicolini, S. Ranise, and D. Zucchelli. Deciding extensions of the theory of arrays by integrating decision procedures and instantiation strategies. In M. Fisher, W. van der Hoek, B. Konev, and A. Lisitsa, editors, Logics in Artificial Intelligence, 10th European Conference, JELIA 2006, Liverpool, UK, September 13-15, 2006, Proceedings, volume 4160 of Lecture Notes in Computer Science, pages 177-189. Springer, 2006.
79. S. Ghilardi, E. Nicolini, and D. Zucchelli. A comprehensive framework for combined decision procedures. In B. Gramlich, editor, Frontiers of Combining Systems, 5th International Workshop, FroCoS 2005, Vienna, Austria, September 19-21, 2005, Proceedings, volume 3717 of Lecture Notes in Computer Science, pages 1-30. Springer, 2005.
80. F. Giunchiglia and R. Sebastiani. Building decision procedures for modal logics from propositional decision procedures - the case study of modal K. In Proc. CADE'13, number 1104 in LNAI. Springer, 1996.
81. D. Hochbaum, N. Megiddo, J. Naor, and A. Tamir. Tight bounds and 2-approximation algorithms for integer programs with two variables per inequality. Mathematical Programming, 62:63-92, 1993.
82. I. Horrocks. The FaCT system. In H. de Swart, editor, Proc. TABLEAUX-98, volume 1397 of LNAI, pages 307-312. Springer, 1998.
83. J. Huang. MUP: a minimal unsatisfiability prover. In Proc. ASPDAC '05. ACM Press, 2005.
84. J. Jaffar, M. J. Maher, P. J. Stuckey, and R. H. C. Yap. Beyond finite domains. In 2nd International Workshop on Principles and Practice of Constraint Programming (PPCP'94), volume 874 of Lecture Notes in Computer Science, pages 86-94, 1994.
85. N. Karmakar. A new polynomial-time algorithm for linear programming. Combinatorica, 4(4):373-395, 1984.
86. S. Krstíc and S. Conchon. Canonization for disjoint unions of theories. In F. Baader, editor, Proceedings of the 19th International Conference on Computer-Aided Deduction (CADE '03), volume 2741 of Lecture Notes in Artificial Intelligence, pages 197-211. Springer, August 2003. Miami Beach, FL.
87. S. Krstíc, A. Goel, J. Grundy, and C. Tinelli. Combined satisfiability modulo parametric theories. In O. Grumberg and M. Huth, editors, Proceedings of the 13th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (Braga, Portugal), volume 4424 of Lecture Notes in Computer Science, pages 618-631. Springer, 2007.
88. R. Kannan and C. L. Monma. On the computational complexity of integer programming problems. In Optimisation and Operations Research, volume 157 of Lecture Notes in Economics and Mathematical Systems, pages 161-172. Springer-Verlag, 1978.
89. D. Kapur, R. Majumdar, and C. G. Zarba. Interpolation for data structures. In Proc. SIGSOFT FSE. ACM, 2006.
90. D. Kroening, J. Ouaknine, S. A. Seshia, and O. Strichman. Abstraction-based satisfiability solving of Presburger arithmetic. In Proc. 16th International Conference on Computer-Aided Verification (CAV), pages 308-320, July 2004.
91. D. Kroening and G. Weissenbacher. Lifting propositional interpolants to the word-level. In Proceedings of FMCAD, pages 85-89. IEEE, 2007.
92. S. K. Lahiri and R. E. Bryant. Deductive verification of advanced out-of-order microprocessors. In Proc. 15th International Conference on Computer-Aided Verification (CAV), volume 2725 of LNCS, pages 341-354, 2003.
93. S. K. Lahiri, R. E. Bryant, A. Goel, and M. Talupur. Revisiting positive equality. In Proc. Tools and Algoriths for the Construction and Analysis of Systems (TACAS), LNCS 2988, pages 1-15, 2004.
94. J. Levitt. Formal Verification Techniques for Digital Systems. PhD thesis, Stanford University, 1999.
95. S. K. Lahiri and M. Musuvathi. An efficient decision procedure for UTVPI constraints. In J. G. Carbonell and J. Siekmann, editors, Proceedings of the 5th International Workshop on Frontiers of Combining Systems (FroCos '05), volume 3717 of Lecture Notes in Artificial Intelligence, pages 168-183. Springer, September 2005.
96. I. Lynce and J. P. Marques-Silva. On computing minimum unsatis fiable cores. In SAT, 2004.
97. S. K. Lahiri and S. A. Seshia. The UCLID decision procedure. In Proc. 16th International Conference on Computer-Aided Verification (CAV), pages 475-478, July 2004.
98. Y. V. Matiyasevich. Diophantine representation of recursively enumerable predicates. In J. E. Fenstad, editor, Second Scandinavian Logic Symposium, volume 63 of Studies in Logic and the Foundations of Mathematics, pages 171-177. North-Holland Publishing Company, 1971.
99. K. McMillan. Applying SAT Methods in Unbounded Symbolic Model Checking. In Proc. CAV '02, number 2404 in LNCS. Springer, 2002.
100. K. McMillan. Interpolation and SAT-based model checking. In Proc. CAV, 2003.
101. K. L. McMillan. An interpolating theorem prover. Theor. Comput. Sci., 345(1), 2005.
102. F. Maric and P. Janicic. ARGO-Lib: A generic platform for decision procedures. In Proceedings of IJCAR '04, volume 3097 of Lecture Notes in Artificial Intelligence, pages 213-217. Springer, 2004.
103. M. Moskal and J. Lopuszánski. Fast quantifier reasoning with lazy proof explication. Technical report, Institute of Computer Science, University of Wroc law, May 2006.
104. M. N. Mneimneh, I. Lynce, Z. S. Andraus, J. P. Marques-Silva, and K. A. Sakallah. A Branch-and-Bound Algorithm for Extracting Smallest Minimal Unsatisfiable Formulas. In Proc. SAT'05, volume 3569 of LNCS. Springer, 2005.
105. M. W. Moskewicz, C. F. Madigan, Y. Zhao, L. Zhang, and S. Malik. Chaff: Engineering an efficient SAT solver. In Design Automation Conference, 2001.
106. M. O. Möller. Solving Bit-Vector Equations - a Decision Procedure for Hardware Verification. PhD thesis, University of Ulm, 1997.
107. Z. Manna and C. Zarba. Combining decision procedures. In Formal Methods at the Crossroads: from Panacea to Foundational Support, volume 2787 of Lecture Notes in Computer Science, pages 381-422. Springer, November 2003.
108. Z. Manna and C. G. Zarba. Combining decision procedures. In Formal Methods at the Cross Roads: From Panacea to Foundational Support, volume 2757 of Lecture Notes in Computer Science, pages 381-422. Springer, 2003.
109. G. Nelson and D. C. Oppen. Simplification by cooperating decision procedures. ACM Trans. on Programming Languages and Systems, 1(2):245-257, October 1979.
110. G. Nelson and D. C. Oppen. Fast decision procedures based on congruence closure. Journal of the Association for Computing Machinery, 27(2):356-364, April 1980.
111. R. Nieuwenhuis and A. Oliveras. Congruence closure with integer offsets. In In 10th Int. Conf. Logic for Programming, Artif. Intell. and Reasoning (LPAR), volume 2850 of LNAI, pages 78-90. Springer, 2003.
112. R. Nieuwenhuis and A. Oliveras. Decision Procedures for SAT, SAT Modulo Theories and Beyond. The BarcelogicTools. (Invited Paper). In G. Sutcliffe and A. Voronkov, editors, 12h International Conference on Logic for Programming, Artificial Intelligence and Reasoning, LPAR'05, volume 3835 of Lecture Notes in Computer Science, pages 23-46. Springer, 2005.
113. R. Nieuwenhuis and A. Oliveras. Proof-Producing Congruence Closure. In Proceedings of the 16th International Conference on Term Rewriting and Applications, RTA'05, volume 3467 of LNCS. Springer, 2005.
114. R. Nieuwenhuis and A. Oliveras. DPLL(T) with exhaustive theory propagation and its application to difference logic. In K. Etessami and S. K. Rajamani, editors, Proceedings of the 17th International Conference on Computer Aided Verification (CAV '05), volume 3576 of Lecture Notes in Computer Science, pages 321-334. Springer, July 2005.
115. R. Nieuwenhuis, A. Oliveras, and C. Tinelli. Abstract DPLL and abstract DPLL modulo theories. In F. Baader and A. Voronkov, editors, Proceedings of the 11th International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR'04), Montevideo, Uruguay, volume 3452 of Lecture Notes in Computer Science, pages 36-50. Springer, 2005.
116. R. Nieuwenhuis, A. Oliveras, and C. Tinelli. Solving SAT and SAT Modulo Theories: from an Abstract Davis-Putnam-Logemann- Loveland Procedure to DPLL(T). Journal of the ACM, 53(6):937-977, November 2006.
117. R. Nieuwenhuis and A. Rubio. Paramodulation-based theorem proving. In J. A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, pages 371-443. Elsevier and MIT Press, 2001.
118. Y. Oh, M. N. Mneimneh, Z. S. Andraus, K. A. Sakallah, and I. L. Markov. Amuse: A Minimally-Unsatisfiable Subformula Extractor. In Proc. DAC'04. ACM/IEEE, 2004.
119. D. C. Oppen. Reasoning about recursively defined data structures. Journal of the Association for Computing Machinery, 27(3):403-411, July 1980.
120. D. C. Oppen. Complexity, convexity and combinations of theories. Theoretical Computer Science, 12:291-302, 1980.
121. C. H. Papadimitriou. On the complexity of integer programming. Journal of the Association for Computing Machinery, 28(4):765-768, 1981.
122. V. Pratt. Two easy theories whose combination is hard. Technical report, Massachusetts Institute of Technology, 1977. Cambridge, MA.
123. A. Pnueli, Y. Rodeh, O. Shtrichman, and M. Siegel. Deciding equality formulas by small domains instantiations. In Proceedings of the 11th International Conference on Computer Aided Verification, vol ume 1633 of Lecture Notes in Computer Science, pages 455-469. Springer, 1999.
124. A. Pnueli, Y. Rodeh, M. Siegel, and O. Strichman. The small model property: How small can it be? Journal of Information and Computation, 178(1):279-293, October 2002.
125. P. F. Patel-Schneider. DLP system description. In Proc. DL-98, pages 87-89, 1998.
126. P. Pudĺak. Lower bounds for resolution and cutting planes proofs and monotone computations. J. of Symbolic Logic, 62(3), 1997.
127. W. Pugh. The omega test: A fast and practical integer programming algorithm for dependence analysis. In Supercomputing, pages 4-13, 1991.
128. C. Ringeissen. Cooperation of decision procedures for the satisfiability problem. In F. Baader and K. Schulz, editors, Frontiers of Combining Systems: Proceedings of the 1st International Workshop, Munich (Germany), Applied Logic, pages 121-140. Kluwer Academic Publishers, March 1996.
129. S. Ranise, C. Ringeissen, and C. G. Zarba. Combining data structures with nonstably infinite theories using many-sorted logic. In B. Gramlich, editor, Proceedings of the Workshop on Frontiers of Combining Systems, volume 3717 of Lecture Notes in Computer Science, pages 48-64. Springer, 2005.
130. H. Ruess and N. Shankar. Deconstructing Shostak. In 16th Annual IEEE Symposium on Logic in Computer Science, pages 19-28. IEEE Computer Society, June 2001. Boston, MA.
131. A. Rybalchenko and V. Sofronie-Stokkermans. Constraint Solving for Interpolation. In VMCAI, LNCS. Springer, 2007.
132. S. A. Seshia and R. E. Bryant. Deciding quantifier-free Presburger formulas using parameterized solution bounds. Logical Methods in Computer Science, 1(2):1-26, December 2005.
133. A. Stump, C. W. Barrett, and D. L. Dill. CVC: A cooperating validity checker. In E. Brinksma and K. G. Larsen, editors, Proceedings of the 14th International Conference on Computer Aided Verification (CAV '02), volume 2404 of Lecture Notes in Computer Science, pages 500-504. Springer, July 2002.
134. A. Stump, D. L. Dill, C. W. Barrett, and J. Levitt. A decision procedure for an extensional theory of arrays. In Proceedings of the 16th IEEE Symposium on Logic in Computer Science (LICS '01), pages 29-37. IEEE Computer Society, June 2001.
135. R. Sebastiani. Lazy Satisfiability Modulo Theories. Journal on Satisfiability, Boolean Modeling and Computation - JSAT., 3, 2007.
136. S. A. Seshia. Adaptive Eager Boolean Encoding for Arithmetic Reasoning in Verification. PhD thesis, Carnegie Mellon University, 2005.
137. R. E. Shostak. An algorithm for reasoning about equality. Communications of the ACM, 21(7), 1978.
138. R. E. Shostak. A practical decision procedure for arithmetic with function symbols. Journal of the ACM, 26(2):351-360, April 1979.
139. R. Shostak. Deciding combinations of theories. Journal of the Association for Computing Machinery, 31(1):1-12, 1984.
140. N. Suzuki and D. Jefferson. Verification decidability of presburger array programs. J. ACM, 27(1):191-205, 1980.
141. S. A. Seshia, S. K. Lahiri, and R. E. Bryant. A hybrid SAT-based decision procedure for separation logic with uninterrupted functions. In 40th Design Automation Conference (DAC '03), pages 425-430, June 2003.
142. N. Shankar and H. Rues. Combining Shostak theories. In S. Tison, editor, Int'l Conf. Rewriting Techniques and Applications (RTA '02), volume 2378 of LNCS, pages 1-18. Springer, 2002.
143. H. M. Sheini and K. A. Sakallah. A scalable method for solving satisfiability of integer linear arithmetic logic. In F. Bacchus and T.Walsh, editors, Proceedings of the 8th International Conference on Theory and Applications of Satisfiability Testing (SAT '05), volume 3569 of Lecture Notes in Computer Science, pages 241-256. Springer, June 2005.
144. H. M. Sheini and K. A. Sakallah. A Progressive Simplifier for Satisfiability Modulo Theories. In Proc. SAT'06, volume 4121 of LNCS. Springer, 2006.
145. O. Strichman, S. A. Seshia, and R. E. Bryant. Deciding separation formulas with SAT. In E. Brinksma and K. G. Larsen, editors, Proc. 14th Intl. Conference on Computer-Aided Verification (CAV'02), LNCS 2404, pages 209-222. Springer-Verlag, July 2002.
146. S. A. Seshia, K. Subramani, and R. E. Bryant. On solving boolean combinations of UTVPI constraints. Journal of Satisfiability, Boolean Modeling, and Computation (JSAT), 3:67-90, 2007.
147. O. Strichman. On solving Presburger and linear arithmetic with SAT. In Formal Methods in Computer-Aided Design (FMCAD '02), LNCS 2517, pages 160-170. Springer-Verlag, November 2002.
148. O. Strichman. Optimizations in decision procedures for propositional linear inequalities. Technical Report CMU-CS-02-133, Carnegie Mellon University, 2002.
149. C. Tinelli and M. T. Harandi. A new correctness proof of the Nelson- Oppen combination procedure. In F. Baader and K. Schulz, editors, Frontiers of Combining Systems: Proceedings of the 1st International Workshop (Munich, Germany), Applied Logic, pages 103-120. Kluwer Academic Publishers, March 1996.
150. C. Tinelli and C. Ringeissen. Unions of non-disjoint theories and combinations of satisfiability procedures. Theoretical Computer Science, 290(1):291-353, January 2003.
151. M. Talupur, N. Sinha, O. Strichman, and A. Pnueli. Range allocation for separation logic. In Proc. Computer-Aided Verification (CAV), volume 3114 of Lecture Notes in Computer Science, pages 148-161, 2004.
152. C. Tinelli and C. Zarba. Combining decision procedures for sorted theories. In J. Alferes and J. Leite, editors, Proceedings of the 9th European Conference on Logic in Artificial Intelligence (JELIA'04), Lisbon, Portugal, volume 3229 of Lecture Notes in Artificial Intelligence, pages 641-653. Springer, 2004.
153. C. Tinelli and C. Zarba. Combining nonstably infinite theories. Journal of Automated Reasoning, 34(3):209-238, April 2005.
154. J. von zur Gathen and M. Sieveking. A bound on solutions of linear integer equalities and inequalities. Proceedings of the American Mathematical Society, 72(1):155-158, October 1978.
155. C. Wang, A. Gupta, and M. Ganai. Predicate learning and selective theory deduction for a difference logic solver. In DAC '06: Proceedings of the 43rd annual conference on Design automation. ACM Press, 2006.
156. S. Wolfman and D. Weld. The LPSAT Engine & its Application to Resource Planning. In Proc. IJCAI, 1999.
157. G. Yorsh and M. Musuvathi. A combination method for generating interpolants. In CADE, volume 3632 of LNCS. Springer, 2005.
158. Y. Yu and S. Malik. Lemma Learning in SMT on Linear Constraints. In Proc. SAT'06, volume 4121 of LNCS. Springer, 2006.
159. J. Zhang, S. Li, and S. Shen. Extracting Minimum Unsatisfiable Cores with a Greedy Genetic Algorithm. In Proc. ACAI, volume 4304 of LNCS. Springer, 2006.
160. L. Zhang and S. Malik. The quest for efficient boolean satisfiability solvers. In Proc. CAV'02, number 2404 in LNCS, pages 17-36. Springer, 2002.
161. L. Zhang and S. Malik. Extracting small unsatisfiable cores from unsatisfiable boolean formula. In Proc. of SAT, 2003.
162. L. Zhang, C. F. Madigan, M. W. Moskewicz, and S. Malik. Efficient conflict driven learning in boolean satisfiability solver. In ICCAD, pages 279-285, 2001.