A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
A machine program for theorem-proving
Communications of the ACM
Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
A New Fast Tableau-Based Decision Procedure for an Unquantified Fragment of Set Theory
Selected Papers from Automated Deduction in Classical and Non-Classical Logics
A Decision Procedure for an Extensional Theory of Arrays
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Efficient theory combination via boolean search
Information and Computation - Special issue: Combining logical systems
SMT-COMP: satisfiability modulo theories competition
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Architecting Solvers for SAT Modulo Theories: Nelson-Oppen with DPLL
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
From KSAT to Delayed Theory Combination: Exploiting DPLL Outside the SAT Domain
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Deciding array formulas with frugal axiom instantiation
SMT '08/BPR '08 Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning
A write-based solver for SAT modulo the theory of arrays
Proceedings of the 2008 International Conference on Formal Methods in Computer-Aided Design
Combining Decision Procedures by (Model-)Equality Propagation
Electronic Notes in Theoretical Computer Science (ENTCS)
Annals of Mathematics and Artificial Intelligence
Theory decision by decomposition
Journal of Symbolic Computation
CAV'07 Proceedings of the 19th international conference on Computer aided verification
On theorem proving for program checking: historical perspective and recent developments
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Satisfiability algorithms for conjunctive queries over trees
Proceedings of the 14th International Conference on Database Theory
Efficient interpolant generation in satisfiability modulo linear integer arithmetic
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
Computing small unsatisfiable cores in satisfiability modulo theories
Journal of Artificial Intelligence Research
Sharing is caring: combination of theories
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Flexible interpolation with local proof transformations
Proceedings of the International Conference on Computer-Aided Design
Combining decision procedures by (model-)equality propagation
Science of Computer Programming
A simplex-based extension of fourier-motzkin for solving linear integer arithmetic
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Abstract conflict driven learning
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Being careful about theory combination
Formal Methods in System Design
A modular approach to MaxSAT modulo theories
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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Lazy algorithms for Satisfiability Modulo Theories (SMT) combine a generic DPLL-based SAT engine with a theory solver for the given theory T that can decide the T-consistency of conjunctions of ground literals. For many theories of interest, theory solvers need to reason by performing internal case splits. Here we argue that it is more convenient to delegate these case splits to the DPLL engine instead. The delegation can be done on demand for solvers that can encode their internal case splits into one or more clauses, possibly including new constants and literals. This results in drastically simpler theory solvers. We present this idea in an improved version of DPLL(T), a general SMT architecture for the lazy approach, and formalize and prove it correct in an extension of Abstract DPLL Modulo Theories, a framework for modeling and reasoning about lazy algorithms for SMT. A remarkable additional feature of the architecture, also discussed in the paper, is that it naturally includes an efficient Nelson-Oppen-like combination of multiple theories and their solvers.