MathSAT: Tight integration of SAT and mathematical decision procedures

Journal of Automated Reasoning

Volumn 35, Issue 1-3, 2005, Pages 265-293

  Bozzano, Marco ^a   Bruttomesso, Roberto ^a   Cimatti, Alessandro ^a   Junttila, Tommi ^b   Van Rossum, Peter ^a   Schulz, Stephan ^c   Sebastiani, Roberto ^d  

^a ITC IRST   (Italy)

^b AALTO UNIVERSITY   (Finland)

^c UNIVERSITY OF VERONA   (Italy)

^d UNIVERSITY OF TRENTO   (Italy)

Author keywords

Integrated decision procedures; Linear arithmetic logic; Propositional satisfiability; Satisfiability module theory

Indexed keywords

BENCHMARKING; BOOLEAN FUNCTIONS; CONSTRAINT THEORY; INTEGRATION; LINEAR PROGRAMMING; MATHEMATICAL MODELS; PROBLEM SOLVING;

INTEGRATED DECISION PROCEDURES; LINEAR ARITHMETIC LOGIC; PROPOSITIONAL SATISFIABILITY; SATISFIABILITY MODULE THEORIES; SATISFIABILITY TECHNIQUES (SAT);

DECISION THEORY;

EID: 33750366082     PISSN: 01687433     EISSN: 15730670     Source Type: Journal    
DOI: 10.1007/s10817-005-9004-z     Document Type: Article

References (44)

1. Armando, A., Castellini, C. and Giunchiglia, E.: SAT-based procedures for temporal reasoning, in Proc. European Conference on Planning, CP-99.
2. Armando, A., Castellini, C., Giunchiglia, E. and Maratea, M.: A SAT-based decision procedure for the boolean combination of difference constraints, in Proc. Conference on Theory and Applications of Satisfiability Testing (SAT04), 2004.
3. Audemard, G., Bertoli, P., Cimatti, A., Kornilowicz, A. and Sebastiani, R.: A SAT based approach for solving formulas over boolean and linear mathematical propositions, in Proc. CADE'2002, Vol. 2392 of LNAI, 2002.
4. Audemard, G., Cimatti, A., Kornilowicz, A. and Sebastiani, R.; SAT-based bounded model checking for timed systems, in Proc. FORTE'02, Vol. 2529 of LNCS, 2002.
5. Badros, G. and Borning, A.: The Cassowary linear arithmetic constraint solving algorithm: interface and implementation. Technical Report UW-CSE-98-06-04, University of Washington, 1998.
6. Ball, T., Cook, B., Lahiri, S. and Zhang, L.: Zapato: Automatic theorem proving for predicate abstraction refinement, in Proc. CAV'04, Vol. 3114 of LNCS, 2004, pp. 457-461.
7. Barrett, C. and Berezin, S.: CVC Lite: A new implementation of the cooperating validity checker, in Proc. CAV'04, Vol. 3114 of LNCS, 2004, pp. 515-518.
8. Bayardo, Jr., R. J. and Schrag, R. C.: Using CSP look-back techniques to solve real-world SAT instances, in Proc. AAAI/IAAI'97, 1997, pp. 203-208.
9. Bockmayr, A. and Weispfenning, V.: Solving numerical constraints, in Handbook of Automated Reasoning, MIT, 2001, pp. 751-842.
10. Borning, A., Marriott, K., Stuckey, P. and Xiao, Y.: Solving linear arithmetic constraints for user interface applications, in Proc. UIST'7, 1997, pp. 87-96.
11. Bozzano, M., Bruttomesso, R., Cimatti, A., Junttila, T., van Rossum, P., Schulz, S. and Sebastiani, R.: An incremental and layered procedure for the satisfiability of linear arithmetic logic, in Proc. TACAS 2005, Vol. 3440 of LNCS, 2005, pp. 317-333.
12. Brinkmann, R. and Drechsler, R.: RTL-Datapath verification using integer linear programming, in Proc. ASP-DAC 2002, 2002, pp. 741-746.
13. Cherkassky, B. and Goldberg, A.: Negative-cycle detection algorithms, Math. Program. 85 (1999), 277-311.
14. Cotton, S., Asarin, E., Maler, O. and Niebert, P.: Some progress in satisfiability checking for difference logic, in Proc. FORMATS-FTRTFT 2004, 2004.
15. CVC. CVC, CVCLITE and SVC. http://verify.stanford.edu/{cvc, CVCL, SVC}.
16. de Moura, L. and Ruess, H.: An experimental evaluation of ground decision procedures, in R. Alur and D. Peled (eds.), Proc. 15th Int. Conf. on Computer Aided Verification-CAV04, Vol. 3114 of LNCS. Boston, Massachusetts, 2004, pp. 162-174.
17. Eén, N. and Sörensson, N.: An extensible SAT-solver, in Theory and Applications of Satisfiability Testing (SAT 2003), Vol. 2919 of LNCS, 2004, pp. 502-518.
18. Filliâtre, J.-C., Owre, S., Ruess, H. and Shankar, N.: ICS: Integrated canonizer and solver, in Proc. CAV'01, Vol. 2102 of LNCS, 2001, pp. 246-249.
19. Flanagan, C., Joshi, R., Ou, X. and Saxe, J.: Theorem proving using lazy proof explication, in Proc. CAV'03, Vol. 2725 of LNCS, 2003, pp. 355-367.
20. Ganzinger, H., Hagen, G., Nieuwenhuis, R., Oliveras, A. and Tinelli, C.: DPLL(T): fast decision procedures, in Proc. CAV'04, Vol. 3114 of LNCS, 2004, pp. 175-188.
21. GMP. GNU Multi Precision Library, http://www.swox.com/gmp.
22. Gomes, C., Selman, B. and Kautz, H.: Boosting combination search through randomization, in Proc. of the Fifteenth National Conf. on Artificial Intelligence, 1998, pp. 431-437.
23. ICS. ICS. http://www.icansolve.com.
24. Jaffar, J., Michaylov, S., Stuckey, P.J. and Yap, R.H.C.: The CLP(R) languages and systems, ACM Trans. Program. Lang. Syst. (TOPLAS) 14(3) (1992), 339-395.
25. Kroening, D., Ouaknine, J., Seshia, S. and Strichman, O.: Abstraction-based satisfiability solving of Presburger arithmetic, in Proc. CAV'04, Vol. 3114 of LNCS, 2004, pp. 308-320.
26. Land, H. and Doig, A.: An automatic method for solving discrete programming problems, Econometrica 28 (1960), 497-520.
27. MATHSAT. MATHSAT. http://mathsat.itc.it.
28. Moskewicz, M. W., Madigan, C. F., Zhao, Y., Zhang, L. and Malik, S.: Chaff engineering an efficient SAT solver, in Proc. DAC'01, 2001, pp. 530-535.
29. Nieuwenhuis, R. and Oliveras, A.: Congruence closure with integer offset, in Proc. 10th LPAR, 2003, pp. 77-89.
30. Omega. Omega, http://www.cs.umd.edu/projects/omega.
31. Parthasarathy, G., Iyer, M., Cheng, K.-T. and Wang, L.-C: An efficient finite-domain constraint solver for circuits, in Proc. DAC'04, 2004, pp. 212-217.
32. SAL. SAL Suite, http://www.csl.sri.com/users/demoura/gdp-benchmark.html.
33. Schulz, S.: E-A Brainiac theorem prover, AI Commun. 15(2/3) (2002), 111-126.
34. SEP. SEP Suite, http://iew3.technion.ac.il/~ofers/smtlib-local/ benchmarks.html.
35. Seshia, S., Lahiri, S. and Bryant, R.: A hybrid SAT-based decision procedure for separation logic with uninterpreted function, in Proc. DAC'03, pp. 425-430.
36. Shin, J.-A. and Davis, E.: Continuous time in a SAT-based planner, in Proc. AAAI-04, 2004, pp. 531-536.
37. Silva, J. P. M. and Sakallah, K. A.: GRASP - A new search algorithm for satisfiability, in Proc. ICCAD'96, 1996, pp. 220-227.
38. Stergiou, K. and Koubarakis, M.: Backtracking algorithms for disjunctions of temporal constraints, Artif. Intell. 120(1) (2000), 81-117.
39. Strichman, O.: On solving presburger and linear arithmetic with SAT, in Proc. of Formal Methods in Computer-Aided Design (FMCAD 2002), 2002.
40. Strichman, O., Seshia, S., Bryant, R.: Deciding separation formulas with SAT, in Proc. of Computer Aided Verification, (CAV'02).
41. TM. TM-LPSAT. http://csl.cs.nyu.edu/~jiae/.
42. TSAT. TSAT++. http://www.ai.dist.unige.it/Tsat.
43. UCLID.UCLID. http://www-2.cs.cmu.edu/~uclid.
44. Zhang, L. and Malik, S.: The quest for efficient boolean satisfiability solves, in Proc. CAV'02, 2002, pp. 17-36.