Abstract
Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrated theory reasoning. The most efficient SMT solvers rely on refutationally incomplete methods for incorporating quantifier reasoning. We describe a calculus and a system that tightly integrates Superposition and DPLL(T). In the calculus, all non-unit ground clauses are delegated to the DPLL(T) core. The integration is tight, dependencies on case splits are tracked as hypotheses in the saturation engine. The hypotheses are discharged during backtracking. The combination is refutationally complete for first-order logic, and its implementation is competitive in performance with E-matching based SMT solvers on problems they are good at.
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References
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, 937–977 (2006)
Detlefs, D., Nelson, G., Saxe, J.B.: Simplify: a theorem prover for program checking. J. ACM 52, 365–473 (2005)
Ge, Y., Barrett, C., Tinelli, C.: Solving quantified verification conditions using satisfiability modulo theories. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603. Springer, Heidelberg (2007)
Moskal, M., Lopuszanski, J., Kiniry, J.R.: E-matching for fun and profit. In: Satisfiability Modulo Theories Workshop (2007)
Dutertre, B., de Moura, L.: A Fast Linear-Arithmetic Solver for DPLL(T). In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 81–94. Springer, Heidelberg (2006)
de Moura, L., Bjørner, N.: Z3: An Efficient SMT Solver. In: TACAS 2008 (2008)
Denney, E., Fischer, B., Schumann, J.: Using automated theorem provers to certify auto-generated aerospace software. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097. Springer, Heidelberg (2004)
Prevosto, V., Waldmann, U.: SPASS+T. In: ESCoR Workshop (2006)
Deharbe, D., Ranise, S.: Satisfiability solving for software verification. International Journal on Software Tools Technology Transfer (to appear, 2008)
Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Handbook of Automated Reasoning, pp. 19–99. MIT Press, Cambridge (2001)
Nieuwenhuis, R., Rubio, A.: Paramodulation-based theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning. MIT Press, Cambridge (2001)
de Moura, L., Bjørner, N.: Relevancy Propagation. Technical Report MSR-TR-2007-140, Microsoft Research (2007)
Graf, P.: Substitution tree indexing. In: Hsiang, J. (ed.) RTA 1995. LNCS, vol. 914. Springer, Heidelberg (1995)
Schulz, S.: Simple and Efficient Clause Subsumption with Feature Vector Indexing. In: ESFOR Workshop (2004)
Baumgartner, P., Fuchs, A., Tinelli, C.: Darwin: A theorem prover for the model evolution calculus. In: ESFOR Workshop (2004)
Gallier, J., Narendran, P., Plaisted, D., Raatz, S., Snyder, W.: An algorithm for finding canonical sets of ground rewrite rules in polynomial time. J. ACM 40 (1993)
Barnett, M., Leino, K.R.M., Schulte, W.: The Spec\(\sharp\) programming system: An overview. In: Barthe, G., Burdy, L., Huisman, M., Lanet, J.-L., Muntean, T. (eds.) CASSIS 2004. LNCS, vol. 3362, pp. 49–69. Springer, Heidelberg (2005)
Schulz, S.: E - a brainiac theorem prover. AI Commun 15, 111–126 (2002)
Weidenbach, C., Brahm, U., Hillenbrand, T., Keen, E., Theobalt, C., Topic, D.: SPASS version 2.0. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, Springer, Heidelberg (2002)
Lynch, C.: SMELS: Satisfiability Modulo Equality with Lazy Superposition. The Dagsthul Seminar on Deduction and Decision Procedures (2007)
Korovin, K., Voronkov, A.: Integrating linear arithmetic into superposition calculus. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 223–237. Springer, Heidelberg (2007)
Fietzke, A.: Labelled splitting. Master’s thesis, Saarland University (2007)
Riazanov, A., Voronkov, A.: Splitting without backtracking. In: IJCAI (2001)
Armando, A., Bonacina, M.P., Ranise, S., Schulz, S.: New results on rewrite-based satisfiability procedures. ACM Transactions on Computational Logic (to appear)
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de Moura, L., Bjørner, N. (2008). Engineering DPLL(T) + Saturation. In: Armando, A., Baumgartner, P., Dowek, G. (eds) Automated Reasoning. IJCAR 2008. Lecture Notes in Computer Science(), vol 5195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71070-7_40
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DOI: https://doi.org/10.1007/978-3-540-71070-7_40
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