Delayed Theory Combination vs. Nelson-oppen for satisfiability modulo theories: A comparative analysis

Annals of Mathematics and Artificial Intelligence

Volumn 55, Issue 1-2, 2009, Pages 63-99

  Bruttomesso, Roberto ^a   Cimatti, Alessandro ^b   Franzen, Anders ^b   Griggio, Alberto ^c   Sebastiani, Roberto ^c  

^a UNIVERSITY OF LUGANO   (Switzerland)

^b ITC IRST   (Italy)

^c UNIVERSITY OF TRENTO   (Italy)

Author keywords

Delayed theory combination; Nelson Oppen; Satisfiability modulo theories

Indexed keywords

EID: 70449585656     PISSN: 10122443     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10472-009-9152-7     Document Type: Article

References (46)

1. Ball, T., Cook, B., Lahiri, S.K., Zhang, L.: Zapato: automatic theorem proving for predicate abstraction refinement. In: Proc. CAV'04. LNCS, vol. 3114. Springer, New York (2004).
2. th International Conference on Computer Aided Verification (CAV '04). LNCS, vol. 3114. Springer, New York (2004).
3. Barrett, C., Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Splitting on demand in SAT modulo theories. In: Proc. LPAR'06. LNAI, vol. 4246. Springer, New York (2006).
4. Barrett, C., Tinelli, C.: Cvc3. In: Proc. CAV'07. LNCS, vol. 4590. Springer, New York (2007).
5. Barrett, C.W., Dill, D.L., Stump, A.: A generalization of Shostak's method for combining decision procedures. In: Frontiers of Combining Systems (FROCOS). Lecture Notes in Artificial Intelligence. Springer, Santa Margherita Ligure (2002).
6. Bonacina, M.P., Ghilardi, S., Nicolini, E., Ranise, S., Zucchelli, D.: Decidability and undecidability results for Nelson-Oppen and rewrite-based decision procedures. In: Proc. of IJCAR'06. LNAI, no. 4130 (2006).
7. Bozzano, M., Bruttomesso, R., Cimatti, A., Franzen, A., Hanna, Z., Khasidashvili, Z., Palti, A., Sebastiani, R.: Encoding RTL constructs for MathSAT: a preliminary report. In: Proc. PDPAR'05. ENTCS, vol. 144. Elsevier, Amsterdam (2006).
8. Bozzano, M., Bruttomesso, R., Cimatti, A., Junttila, T., Rossum, P., Schulz, S., Sebastiani, R.: An incremental and layered procedure for the satisfiability of linear arithmetic logic. In: Proc. TACAS'05. LNCS, vol. 3440. Springer, New York (2005).
9. Bozzano, M., Bruttomesso, R., Cimatti, A., Junttila, T., van Rossum, P., Ranise, S., Sebastiani, R.: Efficient satisfiability modulo theories via delayed theory combination. In: Proc. CAV 2005. LNCS, vol. 3576. Springer, New York (2005).
10. Bozzano, M., Bruttomesso, R., Cimatti, A., Junttila, T., van Rossum, P., Ranise, S., Sebastiani, R.: Efficient theory combination via boolean search. Inf. Comput. 204(10), 1493-1525 (2006).
11. Brinkmann, R., Drechsler, R.: RTL-datapath verification using integer linear programming. In: Proc. ASP-DAC 2002, pp. 741-746. IEEE, Piscataway (2002).
12. Bruttomesso, R., Cimatti, A., Franzén, A., Griggio, A., Sebastiani, R.: Delayed theory combination vs. Nelson-Oppen for satisfiability modulo theories: a comparative analysis. In: Proc. LPAR'06. LNAI, vol. 4246. Springer, New York (2006).
13. Bruttomesso, R., Cimatti, A., Franzen, A., Griggio, A., Sebastiani, R.: The MathSAT 4 SMT solver. In: CAV. LNCS, vol. 5123. Springer, New York (2008).
14. Cotton, S., Maler, O.: Fast and flexible difference logic propagation for DPLL(T). In: Proc. SAT'06. LNCS, vol. 4121. Springer, New York (2006).
15. de Moura, L., Bjørner, N.: Model-based theory combination. In: Proc. of the 5th Workshop on Satisfiability Modulo Theories SMT'07. http://www.lsi.upc.edu/~oliveras/smt07/ (2007).
16. de Moura, L., Owre, S., Ruess, H., Rushby, J., Shankar, N.: The ICS decision procedures for embedded deduction. In: Proc. IJCAR'04. LNCS, vol. 3097, pp. 218-222. Springer, New York (2004).
17. Detlefs, D., Nelson, G., Saxe, J.: Simplify: a theorem prover for program checking. J. ACM 52(3), 365-473 (2005).
18. Dutertre, B., de Moura, L.: A fast linear-arithmetic solver for DPLL(T). In: Proc. CAV'06. LNCS, vol. 4144. Springer, New York (2006).
19. Dutertre, B., de Moura, L.: System description: Yices 1.0. In: Proc. on 2nd SMT competition, SMT-COMP'06. yices.csl.sri.com/yices-smtcomp06.pdf (2006).
20. Enderton, H.: A Mathematical Introduction to Logic. Academic, London (1972).
21. Filliâtre, J.-C., Owre, S., Rueß, H., Shankar, N.: ICS: Integrated Canonizer and Solver. In: Proc. CAV'2001 (2001).
22. Flanagan, C., Joshi, R., Ou, X., Saxe, J.B.: Theorem proving using lazy proof explication. In: Proc. CAV 2003. LNCS. Springer, New York (2003).
23. Fontaine, P., Ranise, S., Zarba, C.G.: Combining lists with non-stably infinite theories. In: Proc. LPAR'04. LNCS, vol. 3452. Springer, New York (2004).
24. Ganzinger, H., Hagen, G., Nieuwenhuis, R., Oliveras, A., Tinelli, C.: DPLL(T): fast decision procedures. In: Proc. CAV'04. LNCS, vol. 3114, pp. 175-188. Springer, New York (2004).
25. Ghilardi, S.: Model theoretic methods in combined constraint satisfiability. J. Autom. Reason. 33(3), 221-249 (2004).
26. Ghilardi, S., Nicolini, E., Zucchelli, D.: A comprehensive framework for combined decision procedures. In: Proc. FroCos'05. LNCS, vol. 3717. Springer, New York (2005).
27. Krstic, S., Goel, A.: Architecting solvers for SAT modulo theories: Nelson-Oppen with DPLL. In: Proc. Frontiers of Combining Systems, 6th International Symposium, FroCoS 2007. LNAI, vol. 4720. Springer, New York (2007).
28. Krstić, S., Goel, A., Grundy, J., Tinelli, C.: Combined satisfiability modulo parametric theories. In: TACAS'07. LNCS, vol. 4424. Springer, New York (2007).
29. Lahiri, S.K., Musuvathi, M.: An efficient decision procedure for UTVPI constraints. In: Proc. of 5th International Workshop on Frontiers of Combining Systems (FroCos '05). LNCS, vol. 3717. Springer, New York (2005).
30. Nelson, C.G., Oppen, D.C.: Simplification by cooperating decision procedures. TOPLAS 1(2), 245-257 (1979).
31. Nieuwenhuis, R., Oliveras, A.: Congruence closure with integer offsets. In: Proc. 10th LPAR. LNAI, no. 2850, pp. 77-89. Springer, New York (2003).
32. Nieuwenhuis, R., Oliveras, A.: DPLL(T) with exhaustive theory propagation and its application to difference logic. In: Proc. CAV'05. LNCS, vol. 3576. Springer, New York (2005).
33. Oppen, D.C.: Complexity, convexity and combinations of theories. Theor. Comp. Sci. 12, 291-302 (1980).
34. Ranise, S., Ringeissen, C., Zarba, C.G.: Combining data structures with nonstably infinite theories using many-sorted logic. In: Proc FroCos'05. LNCS, vol. 3717. Springer, New York (2005).
35. Rueß, H., Shankar, N.: Deconstructing Shostak. In: Proc. LICS '01. IEEE Computer Society, Piscataway (2001).
36. Sebastiani, R.: Lazy satisfiability modulo theories. Journal on Satisfiability, Boolean Modeling and Computation, JSAT. 3, 141-224 (2007).
37. Shankar, N., Rueß, H.: Combining Shostak theories. Invited paper for Floc'02/RTA'02 (2002).
38. Shostak, R.: A pratical decision procedure for arithmetic with function symbols. J. ACM 26(2), 51-360 (1979).
39. Shostak, R.: Deciding combinations of theories. J. ACM 31, 1-12 (1984).
40. Tinelli, C., Harandi, M.T.: A new correctness proof of the Nelson-Oppen combination procedure. In: Proc. Frontiers of Combining Systems, FroCoS'06. Applied Logic. Kluwer, Dordrecht (1996).
41. Tinelli, C., Ringeissen, C.: Unions of non-disjoint theories and combinations of satisfiability procedures. Theor. Comp. Sci. 290(1), 291-353 (2003).
42. Tinelli, C., Zarba, C.: Combining nonstably infinite theories. J. Autom. Reason. 34(3), 209-238 (2005).
43. Zarba, C.G.: A tableau calculus for combining non-disjoint theories. In: Proc. Tableaux'02. Lecture Notes in Computer Science, vol. 2381, pp. 315-329. Springer, New York (2002).
44. Zarba, C.G.: Combining sets with integers. In: FroCos'02. Lecture Notes in Computer Science, vol. 2309, pp. 103-116. Springer, New York (2002).
45. Zhang, L., Madigan, C.F., Moskewicz, M.H., Malik, S.: Efficient conflict driven learning in a boolean satisfiability solver. In: Proc. ICCAD '01. IEEE, Piscataway (2001).
46. Zhang, L., Malik, S.: The quest for efficient boolean satisfiability solvers. In: Proc. CAV'02. LNCS, no. 2404, pp. 17-36. Springer, New York (2002).