A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Deciding Separation Formulas with SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Predicate learning and selective theory deduction for a difference logic solver
Proceedings of the 43rd annual Design Automation Conference
A theory-based decision heuristic for DPLL(T)
Proceedings of the 2008 International Conference on Formal Methods in Computer-Aided Design
Effective preprocessing in SAT through variable and clause elimination
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Efficient satisfiability modulo theories via delayed theory combination
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Integrating linear arithmetic into superposition calculus
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Natural domain SMT: a preliminary assessment
FORMATS'10 Proceedings of the 8th international conference on Formal modeling and analysis of timed systems
Cutting to the Chase solving linear integer arithmetic
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Solving systems of linear inequalities by bound propagation
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Quantifier elimination by lazy model enumeration
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Linear quantifier elimination as an abstract decision procedure
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Numeric bounds analysis with conflict-driven learning
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
A method for symbolic computation of abstract operations
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Abstract conflict driven learning
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
QF BV model checking with property directed reachability
Proceedings of the Conference on Design, Automation and Test in Europe
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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The DPLL approach to the Boolean satisfiability problem (SAT) is a combination of search for a satisfying assignment and logical deduction, in which each process guides the other. We show that this approach can be generalized to a richer class of theories. In particular, we present an alternative to lazy SMT solvers, in which DPLL is used only to find propositionally satisfying assignments, whose feasibility is checked by a separate theory solver. Here, DPLL is applied directly to the theory. We search in the space of theory structures (for example, numerical assignments) rather than propositional assignments. This makes it possible to use conflict in model search to guide deduction in the theory, much in the way that it guides propositional resolution in DPLL. Some experiments using linear rational arithmetic demonstrate the potential advantages of the approach.