Abstract
An overview is given of a number of recent developments in SAT and SAT Modulo Theories (SMT). In particular, based on our framework of Abstract DPLL and Abstract DPLL modulo Theories, we explain our DPLL(T) approach to SMT.
Experimental results and future projects are discussed within BarcelogicTools, a set of logic-based tools developed by our research group in Barcelona. At the 2005 SMT competition, BarcelogicTools won all four categories it participated in (out of the seven existing categories).
Parts of this work were published in a preliminary form in, [NO03,GHN+04,NOT05] [NO05c,NO05b,NO05a] several of them in collaboration with Cesare Tinelli.
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Audemard, G., Bertoli, P., Cimatti, A., Kornilowicz, A., Sebastiani, R.: A SAT based approach for solving formulas over boolean and linear mathematical propositions. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 195–210. Springer, Heidelberg (2002)
Armando, A., Castellini, C., Giunchiglia, E.: SAT-based procedures for temporal reasoning. In: Biundo, S., Fox, M. (eds.) ECP 1999. LNCS, vol. 1809, pp. 97–108. Springer, Heidelberg (2000)
Armando, A., Castellini, C., Giunchiglia, E., Maratea, M.: A SAT-based Decision Procedure for the Boolean Combination of Difference Constraints. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 16–29. Springer, Heidelberg (2005)
Ackermann, W.: Solvable Cases of the Decision Problem. Studies in Logic and the Foundations of Mathematics. North-Holland, Amsterdam (1954)
Alur, R.: Timed automata. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 8–22. Springer, Heidelberg (1999)
Barrett, C.W.: Checking Validity of Quantifier-Free Formulas in Combinations of First-Order Theories. PhD thesis, Stanford University (2003)
Barrett, C.W., Berezin, S.: CVC lite: A new implementation of the cooperating validity checker category b. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 515–518. Springer, Heidelberg (2004)
Bozzano, M., Bruttomesso, R., Cimatti, A., Junttila, T.A., van Rossum, P., Schulz, S., Sebastiani, R.: An incremental and layered procedure for the satisfiability of linear arithmetic logic. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 317–333. Springer, Heidelberg (2005)
Bozzano, M., Bruttomesso, R., Cimatti, A., Junttila, T.A., Ranise, S., van Rossum, P., Sebastiani, R., Sebastiani, R., Sebastiani, R.: Efficient satisfiability modulo theories via delayed theory combination. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 335–349. Springer, Heidelberg (2005)
Ball, T., Cook, B., Lahiri, S.K., Zhang, L.: Zapato: Automatic theorem proving for predicate abstraction refinement. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 457–461. Springer, Heidelberg (2004)
Burch, J.R., Dill, D.L.: Automatic verification of pipelined microprocessor control. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 68–80. Springer, Heidelberg (1994)
Barrett, C., Dill, D.L., 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)
Barrett, C., de Moura, L., Stump, A.: SMT-COMP: Satisfiability Modulo Theories Competition. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 20–23. Springer, Heidelberg (2005)
Barrett, C., Dill, D., Stump, A.: Checking satisfiability of first-order formulas by incremental translation into sat. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, p. 236. Springer, Heidelberg (2002)
Bonet, M.L., Esteban, J.L., Galesi, N., Johannsen, J.: On the relative complexity of resolution refinements and cutting planes proof systems. SIAM J. Comput. 30(5), 1462–1484 (2000)
Bryant, R., German, S., Velev, M.: Processor verification using efficient reductions of the logic of uninterpreted functions to propositional logic. ACM Trans. Computational Logic 2(1), 93–134 (2001)
Beame, P., Kautz, H., Sabharwal, A.: On the power of clause learning. In: Proceedings of IJCAI 2003, 18th International Joint Conference on Artificial Intelligence, Acapulco, MX (2003)
Bryant, R.E., Velev, M.N.: Boolean satisfiability with transitivity constraints. ACM Trans. Computational Logic 3(4), 604–627 (2002)
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Comm. of the ACM 5(7), 394–397 (1962)
de Moura, L., Rueß, H.: Lemmas on demand for satisfiability solvers. In: Procs. 5th Int. Symp. on the Theory and Applications of Satisfiability Testing, SAT 2002, pp. 244–251 (2002)
de Moura, L., Rueß, H.: An experimental evaluation of ground decision procedures. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 162–174. Springer, Heidelberg (2004)
de Moura, L., Rueß, H., Shankar, N.: Justifying equality. In: Proceedings of the Second Workshop on Pragmatics of Decision Procedures in Automated Reasoning, Cork, Ireland (2004)
Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM 7, 201–215 (1960)
Downey, P.J., Sethi, R., Tarjan, R.E.: Variations on the common subexpressions problem. J. of the Association for Computing Machinery 27(4), 758–771 (1980)
Eén, N., Sörensson, N.: An extensible sat-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Flanagan, C., Joshi, R., Ou, X., Saxe, J.B.: Theorem proving using lazy proof explanation. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 355–367. Springer, Heidelberg (2003)
Filliâtre, J.-C., Owre, S., Rueß, H., Shankar, N.: ICS: Integrated Canonization and Solving (Tool prese ntation). In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 246–249. Springer, Heidelberg (2001)
Ganzinger, H., Hagen, G., Nieuwenhuis, R., Oliveras, A., Tinelli, C.: DPLL(T): Fast Decision Procedures. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 175–188. Springer, Heidelberg (2004)
Goldberg, E., Novikov, Y.: BerkMin: A fast and robust SAT-solver. In: Design, Automation, and Test in Europe (DATE 2002), pp. 142–149 (2002)
Lahiri, S.K., Seshia, S.A.: The uclid decision procedure. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 475–478. Springer, Heidelberg (2004)
Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: Proc. 38th Design Automation Conference, DAC 2001 (2001)
Manolios, P., Srinivasan, S.K.: A computationally efficient method based on commitment refinement maps for verifying pipelined machines. In: ACM IEEE Int. Conf. on Formal Methods and Models for Co-Design, MEMOCODE (2005)
Manolios, P., Srinivasan, S.K.: Refinement maps for efficient verification of processor models. In: Design, Automation and Test in Europe Conference and Exposition (DATE), pp. 1304–1309. IEEE Computer Society Press, Los Alamitos (2005)
Marques-Silva, J., Sakallah, K.A.: GRASP: A search algorithm for propositional satisfiability. IEEE Trans. Comput. 48(5), 506–521 (1999)
Nelson, G., Oppen, D.C.: Simplification by cooperating decision procedures. ACM Trans. Program. Lang. Syst. 1(2), 245–257 (1979)
Nieuwenhuis, R., Oliveras, A.: Congruence Closure with Integer Offsets. In: Y. Vardi, M., Voronkov, A. (eds.) LPAR 2003. LNCS (LNAI), vol. 2850, pp. 78–90. Springer, Heidelberg (2003)
Nieuwenhuis, R., Oliveras, A.: BarcelogicTools for SMT. In: SMT Competition 2005. Entrants’ system descriptions (July 2005), www.csl.sri.com/users/demoura/smt-comp
Nieuwenhuis, R., Oliveras, A.: DPLL(T) with Exhaustive Theory Propagation and its Application to Difference Logic. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 321–334. Springer, Heidelberg (2005)
Nieuwenhuis, R., Oliveras, A.: Proof-Producing Congruence Closure. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 453–468. Springer, Heidelberg (2005)
Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Abstract DPLL and Abstract DPLL Modulo Theories. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 36–50. Springer, Heidelberg (2005)
Ranise, S., Tinelli, C.: The SMT-LIB Format: An Initial Proposal. In: Proceedings of the 1st Workshop on Pragmatics of Decision Procedures in Automated Reasoning, Miami (2003)
Ryan, L.: Efficient Algorithms for Clause-Learning SAT Solvers. Master’s thesis, School of Computing Science, Simon Fraser University (2004)
Shostak, R.E.: Deciding combinations of theories. Journal of the ACM 31(1), 1–12 (1984)
Stump, A., Tan, L.-Y.: The algebra of equality proofs. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 469–483. Springer, Heidelberg (2005)
Strichman, O.: On solving presburger and linear arithmetic with sat. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 160–170. Springer, Heidelberg (2002)
Zhang, L., Madigan, C.F., Moskewicz, M.W., Malik, S.: Efficient conflict driven learning in a Boolean satisfiability solver. In: Int. Conf. on Computer-Aided Design (ICCAD 2001), pp. 279–285 (2001)
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Nieuwenhuis, R., Oliveras, A. (2005). Decision Procedures for SAT, SAT Modulo Theories and Beyond. The BarcelogicTools. In: Sutcliffe, G., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2005. Lecture Notes in Computer Science(), vol 3835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11591191_3
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DOI: https://doi.org/10.1007/11591191_3
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