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
ACM Transactions on Computational Logic (TOCL)
Finding bugs with a constraint solver
Proceedings of the 2000 ACM SIGSOFT international symposium on Software testing and analysis
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Lazy Theorem Proving for Bounded Model Checking over Infinite Domains
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
The Quest for Efficient Boolean Satisfiability Solvers
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
A hybrid SAT-based decision procedure for separation logic with uninterpreted functions
Proceedings of the 40th annual Design Automation Conference
APAQS '00 Proceedings of the The First Asia-Pacific Conference on Quality Software (APAQS'00)
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
A Decision Procedure for an Extensional Theory of Arrays
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
MathSAT: Tight Integration of SAT and Mathematical Decision Procedures
Journal of Automated Reasoning
Modular proof systems for partial functions with Evans equality
Information and Computation - Special issue: Combining logical systems
Efficient theory combination via boolean search
Information and Computation - Special issue: Combining logical systems
Rewrite-Based Satisfiability Procedures for Recursive Data Structures
Electronic Notes in Theoretical Computer Science (ENTCS)
Rewrite-Based Decision Procedures
Electronic Notes in Theoretical Computer Science (ENTCS)
Decision procedures for extensions of the theory of arrays
Annals of Mathematics and Artificial Intelligence
On Variable-inactivity and Polynomial T-Satisfiability Procedures
Journal of Logic and Computation
Model-based Theory Combination
Electronic Notes in Theoretical Computer Science (ENTCS)
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
A taxonomy of theorem-proving strategies
Artificial intelligence today
Splitting on demand in SAT modulo theories
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Automatic combinability of rewriting-based satisfiability procedures
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Decidability and undecidability results for nelson-oppen and rewrite-based decision procedures
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Invited contribution: a comprehensive framework for combined decision procedures
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
An efficient decision procedure for UTVPI constraints
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
What's decidable about arrays?
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Yet another decision procedure for equality logic
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
On Deciding Satisfiability by DPLL($\Gamma+{\mathcal T}$) and Unsound Theorem Proving
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
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
Instantiation of SMT problems modulo integers
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
On Deciding Satisfiability by Theorem Proving with Speculative Inferences
Journal of Automated Reasoning
Modular termination and combinability for superposition modulo counter arithmetic
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
An Instantiation Scheme for Satisfiability Modulo Theories
Journal of Automated Reasoning
A calculus for generating ground explanations
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
SMELS: Satisfiability Modulo Equality with Lazy Superposition
Journal of Automated Reasoning
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The topic of this article is decision procedures for satisfiability modulo theories (SMT) of arbitrary quantifier-free formulae. We propose an approach that decomposes the formula in such a way that its definitional part, including the theory, can be compiled by a rewrite-based first-order theorem prover, and the residual problem can be decided by an SMT-solver, based on the Davis-Putnam-Logemann-Loveland procedure. The resulting decision by stages mechanism may unite the complementary strengths of first-order provers and SMT-solvers. We demonstrate its practicality by giving decision procedures for the theories of records, integer offsets and arrays, with or without extensionality, and for combinations including such theories.