Abstract
Finding small unsatisfiable cores for SAT problems has recently received a lot of interest, mostly for its applications in formal verification. Surprisingly, the same problem in the context of SAT Modulo Theories (SMT) has instead received very little attention in the literature; in particular, we are not aware of any work aiming at producing small unsatisfiable cores in SMT.
The purpose of this paper is to start filling the gap in this area, by proposing a novel approach for computing small unsat cores in SMT. The main idea is to combine an SMT solver with an external propositional core extractor: the SMT solver produces the theory lemmas found during the search; the core extractor is then called on the boolean abstraction of the original SMT problem and of the theory lemmas. This results in an unsatisfiable core for the original SMT problem, once the remaining theory lemmas have been removed.
The approach has several advantages: it is extremely simple to implement and to update, and it can be interfaced with every propositional core extractor in a plug-and-play way, so that to benefit for free of all unsat-core reduction techniques which have been or will be made available.
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References
Barrett, C., Berezin, S.: CVC Lite: A New Implementation of the Cooperating Validity Checker. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, Springer, Heidelberg (2004)
Bozzano, M., et al.: 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)
Cimatti, A., Griggio, A., Sebastiani, R.: A Simple and Flexible Way of Computing Small Unsatisfiable Cores in SAT Modulo Theories. Technical Report DIT-07-006, DIT, Univ. of Trento (2007), Extended version. Available at http://dit.unitn.it/~griggio/papers/sat07_extended.pdf .
Dershowitz, N., Hanna, Z., Nadel, A.: A Scalable Algorithm for Minimal Unsatisfiable Core Extraction. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 36–41. Springer, Heidelberg (2006)
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, Springer, Heidelberg (2006)
Ganzinger, H., et al.: DPLL(T): Fast decision procedures. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, Springer, Heidelberg (2004)
Gershman, R., Koifman, M., Strichman, O.: Deriving Small Unsatisfiable Cores with Dominators. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, Springer, Heidelberg (2006)
Lynce, I., Marques Silva, J.P.: On computing minimum unsatisfiable cores. In: Proc. SAT’04 (2004)
Marques-Silva, J., et al.: A Branch-and-Bound Algorithm for Extracting Smallest Minimal Unsatisfiable Formulas. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 467–474. Springer, Heidelberg (2005)
Zhang, J., Li, S., Shen, S.: Extracting Minimum Unsatisfiable Cores with a Greedy Genetic Algorithm. In: Proc. ACAI’06 (2006)
Zhang, L., Malik, S.: Extracting small unsatisfiable cores from unsatisfiable boolean formula. In: Proc. SAT’03 (2003)
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Cimatti, A., Griggio, A., Sebastiani, R. (2007). A Simple and Flexible Way of Computing Small Unsatisfiable Cores in SAT Modulo Theories. In: Marques-Silva, J., Sakallah, K.A. (eds) Theory and Applications of Satisfiability Testing – SAT 2007. SAT 2007. Lecture Notes in Computer Science, vol 4501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72788-0_32
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DOI: https://doi.org/10.1007/978-3-540-72788-0_32
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