Theoretical Computer Science
Boosting combinatorial search through randomization
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Using Reflection to Build Efficient and Certified Decision Procedures
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
A DPLL-Based Calculus for Ground Satisfiability Modulo Theories
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
FDPLL - A First Order Davis-Putnam-Longeman-Loveland Procedure
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Constraint Logic Programming with Hereditary Harrop formulas
Theory and Practice of Logic Programming
The model evolution calculus as a first-order DPLL method
Artificial Intelligence
Towards understanding and harnessing the potential of clause learning
Journal of Artificial Intelligence Research
Focusing and polarization in linear, intuitionistic, and classical logics
Theoretical Computer Science
Improving Coq propositional reasoning using a lazy CNF conversion scheme
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Program verification through characteristic formulae
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Model evolution with equality modulo built-in theories
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Extending Sledgehammer with SMT solvers
CADE'11 Proceedings of the 23rd international conference on Automated deduction
SMT solvers: new oracles for the HOL theorem prover
International Journal on Software Tools for Technology Transfer (STTT) - VSTTE 2009
Effective preprocessing in SAT through variable and clause elimination
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
A modular integration of SAT/SMT solvers to coq through proof witnesses
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Modular SMT proofs for fast reflexive checking inside coq
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Incorporating tables into proofs
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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We describe how the Davis-Putnam-Logemann-Loveland procedure DPLL is bisimilar to the goal-directed proof-search mechanism described by a standard but carefully chosen sequent calculus. We thus relate a procedure described as a transition system on states to the gradual completion of incomplete proof-trees. For this we use a focused sequent calculus for polarised classical logic, for which we allow analytic cuts. The focusing mechanisms, together with an appropriate management of polarities, then allows the bisimulation to hold: The class of sequent calculus proofs that are the images of the DPLL runs finishing on UNSAT, is identified with a simple criterion involving polarities. We actually provide those results for a version DPLL(T) of the procedure that is parameterised by a background theory T for which we can decide whether conjunctions of literals are consistent. This procedure is used for Satisfiability Modulo Theories (SMT) generalising propositional SAT. For this, we extend the standard focused sequent calculus for propositional logic in the same way DPLL(T) extends DPLL: with the ability to call the decision procedure for T. DPLL(T) is implemented as a plugin for Psyche, a proof-search engine for this sequent calculus, to provide a sequent-calculus based SMT-solver.