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A Computing Procedure for Quantification Theory
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A machine program for theorem-proving
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Deciding Separation Formulas with SAT
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Using unsatisfiable cores to debug multiple design errors
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An approach for extracting a small unsatisfiable core
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Efficient Generation of Unsatisfiability Proofs and Cores in SAT
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An abstraction-based decision procedure for bit-vector arithmetic
International Journal on Software Tools for Technology Transfer (STTT)
Automatic abstraction without counterexamples
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A simple and flexible way of computing small unsatisfiable cores in SAT modulo theories
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
CAV'07 Proceedings of the 19th international conference on Computer aided verification
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Boosting minimal unsatisfiable core extraction
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Splitting on demand in SAT modulo theories
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A branch-and-bound algorithm for extracting smallest minimal unsatisfiable formulas
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A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
A scalable algorithm for minimal unsatisfiable core extraction
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Extracting minimum unsatisfiable cores with a greedy genetic algorithm
AI'06 Proceedings of the 19th Australian joint conference on Artificial Intelligence: advances in Artificial Intelligence
S2PF: speculative symbolic PathFinder
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TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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ACM SIGOPS 24th Symposium on Operating Systems Principles
Towards optimization-safe systems: analyzing the impact of undefined behavior
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A modular approach to MaxSAT modulo theories
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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The problem of finding small unsatisfiable cores for SAT formulas has recently received a lot of interest, mostly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many interesting verification problems, which can be more naturally addressed in the framework of Satisfiability Modulo Theories, SMT. Surprisingly, the problem of finding unsatisfiable cores in SMT has received very little attention in the literature. In this paper we present a novel approach to this problem, called the Lemma-Lifting approach. 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, dynamically lifting the suitable amount of theory information to the Boolean level. 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 are removed. The approach is conceptually interesting, and has several advantages in practice. In fact, it is extremely simple to implement and to update, and it can be interfaced with every propositional core extractor in a plug-and-play manner, so as to benefit for free of all unsat-core reduction techniques which have been or will be made available. We have evaluated our algorithm with a very extensive empirical test on SMT-LIB benchmarks, which confirms the validity and potential of this approach.