Deciding Effectively Propositional Logic Using DPLL and Substitution Sets
Tóm tắt
We introduce a DPLL calculus that is a decision procedure for the Bernays-Schönfinkel class, also known as EPR. Our calculus allows combining techniques for efficient propositional search with data-structures, such as Binary Decision Diagrams, that can efficiently and succinctly encode finite sets of substitutions and operations on these. In the calculus, clauses comprise of a sequence of literals together with a finite set of substitutions; truth assignments are also represented using substitution sets. The calculus works directly at the level of sets, and admits performing simultaneous constraint propagation and decisions, resulting in potentially exponential speedups over existing approaches.
Tài liệu tham khảo
Andersen, H.R., Hulgaard, H.: Boolean expression diagrams. Inf. Comput. 179(2), 194–212 (2002)
Baumgartner, P.: Logical engineering with instance-based methods. In: Pfenning, F. (ed.) Automated Deduction—CADE-21, 21st International Conference on Automated Deduction, Bremen, Germany, 17–20 July, 2007, Proceedings. Lecture Notes in Computer Science, vol. 4603, pp. 404–409. Springer (2007)
Baumgartner, P., Fuchs, A., Tinelli, C.: Implementing the model evolution calculus. Int. J. Artif. Intell. Tools 15(1), 21–52 (2006)
Baumgartner, P., Fuchs, A., Tinelli, C.: Lemma learning in the model evolution calculus. In: Hermann, M., Voronkov, A. (eds.) LPAR. Lecture Notes in Computer Science, vol. 4246, pp. 572–586. Springer, New York (2006)
Baumgartner, P., Tinelli, C.: The model evolution calculus as a first-order DPLL method. Artif. Intell. 172(4–5), 591–632 (2008)
Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. C-35(8), 677–691 (1986)
Claessen, K., Sörensson, N.: New techniques that improve mace-style finite model finding. In: CADE-19 Workshop: Model Computation—Principles, Algorithms, Applications (2003)
de Moura, L., Bjørner, N.: Deciding effectively propositional logic using DPLL and substitution sets. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008 (2008)
de Nivelle, H., Meng, J.: Geometric resolution: a proof procedure based on finite model search. In: Furbach, U., Shankar, N. (eds.) IJCAR. Lecture Notes in Computer Science, vol. 4130, pp. 303–317. Springer, New York (2006)
Dershowitz, N., Hanna, Z., Katz, J.: Bounded model checking with QBF. In: Bacchus, F., Walsh, T. (eds.) SAT. Lecture Notes in Computer Science, vol. 3569, pp. 408–414. Springer, New York (2005)
Eén, N., Sörensson, N.: An extensible sat-solver. In: Proceedings of the Sixth International Conference on Theory and Applications of Satisfiability Testing (SAT), pp. 502–518 (2003)
Fermüller, C.G., Leitsch, A., Hustadt, U., Tammet, T.: Resolution decision procedures. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 1791–1849. Elsevier and MIT, Amsterdam (2001)
Gallo, G., Rago, G.: The satisfiability problem for the Schönfinkel-Bernays fragment: partial instantiation and hypergraph algorithms. Technical report 4/94, Dip. Informatica, Universit‘a di Pisa (1994)
Ganzinger, H., Korovin, K.: New directions in instantiation-based theorem proving. In: LICS, pp. 55–64. IEEE Computer Society, Los Alamitos (2003)
Krstic, S., Goel, A.: Architecting solvers for SAT modulo theories: Nelson-Oppen with DPLL. In: Konev, B., Wolter, F. (eds.) FroCos. Lecture Notes in Computer Science, vol. 4720, pp. 1–27. Springer, New York (2007)
Lewis, H.R.: Complexity results for classes of quantificational formulas. J. Comput. Syst. Sci. 21(3), 317–353 (1980)
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)
Pérez, J.A.N., Voronkov, A.: Encodings of bounded LTL model checking in effectively propositional logic. In: Pfenning, F. (ed.) Automated Deduction—CADE-21, 21st International Conference on Automated Deduction, Bremen, Germany, 17–20 July, 2007, Proceedings. Lecture Notes in Computer Science, vol. 4603, pp. 346–361. Springer, New York (2007)
Pérez, J.A.N., Voronkov, A.: Proof systems for effectively propositional logic. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008 (2008)
Piskac, R., de Moura, L., Bjørner, N.: Deciding effectively propositional logic with equality. Technical report MSR-2008-161, Microsoft Research (2008)
Tammet, T., Kadarpik, V.: Combining an inference engine with database: a rule server. In: Schroeder, M., Wagner, G. (eds.) RuleML. Lecture Notes in Computer Science, vol. 2876, pp. 136–149. Springer, New York (2003)
Voronkov, A.: Merging relational database technology with constraint technology. In: Bjørner, D., Broy, M., Pottosin, I.V. (eds.) Ershov Memorial Conference. Lecture Notes in Computer Science, vol. 1181, pp. 409–419. Springer, New York (1996)
Whaley, J., Avots, D., Carbin, M., Lam, M.S.: Using datalog with binary decision diagrams for program analysis. In: Yi, K. (ed.) APLAS. Lecture Notes in Computer Science, vol. 3780, pp. 97–118. Springer, New York (2005)