Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
A machine program for theorem-proving
Communications of the ACM
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
A Generalization of Shostak's Method for Combining Decision Procedures
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
The Quest for Efficient Boolean Satisfiability Solvers
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An interpolating theorem prover
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
MathSAT: Tight Integration of SAT and Mathematical Decision Procedures
Journal of Automated Reasoning
Interpolation for data structures
Proceedings of the 14th ACM SIGSOFT international symposium on Foundations of software engineering
Efficient theory combination via boolean search
Information and Computation - Special issue: Combining logical systems
Fast congruence closure and extensions
Information and Computation
Stepping forward with interpolants in unbounded model checking
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
Interpolant Learning and Reuse in SAT-Based Model Checking
Electronic Notes in Theoretical Computer Science (ENTCS)
The software model checker Blast: Applications to software engineering
International Journal on Software Tools for Technology Transfer (STTT)
Lifting Propositional Interpolants to the Word-Level
FMCAD '07 Proceedings of the Formal Methods in Computer Aided Design
Decision Procedures: An Algorithmic Point of View
Decision Procedures: An Algorithmic Point of View
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
CSIsat: Interpolation for LA+EUF
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Interpolants for Linear Arithmetic in SMT
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Ground Interpolation for the Theory of Equality
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Efficient Craig interpolation for linear Diophantine (dis)equations and linear modular equations
Formal Methods in System Design
Interpolant Generation for UTVPI
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Ground Interpolation for Combined Theories
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Annals of Mathematics and Artificial Intelligence
Constraint solving for interpolation
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Verifying propositional unsatisfiability: pitfalls to avoid
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Array abstractions from proofs
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Efficient interpolant generation in satisfiability modulo theories
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Zap: automated theorem proving for software analysis
LPAR'05 Proceedings of the 12th 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
Lazy abstraction with interpolants
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Interpolation in local theory extensions
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
An efficient decision procedure for UTVPI constraints
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Interpolant-based transition relation approximation
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
DPLL(T) with exhaustive theory propagation and its application to difference logic
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
A combination method for generating interpolants
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Fast and flexible difference constraint propagation for DPLL(T)
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Efficient abstraction refinement in interpolation-based unbounded model checking
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
A practical and complete approach to predicate refinement
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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
Interpolation-based software verification with WOLVERINE
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Effective word-level interpolation for software verification
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
Solving recursion-free horn clauses over LI+UIF
APLAS'11 Proceedings of the 9th Asian conference on Programming Languages and Systems
Whale: an interpolation-based algorithm for inter-procedural verification
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
From under-approximations to over-approximations and back
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Interpolant strength revisited
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Software model checking via IC3
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
When boolean satisfiability meets gaussian elimination in a simplex way
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
An interpolation based crossover operator for genetic programming
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
Lemma localization: a practical method for downsizing SMT-interpolants
Proceedings of the Conference on Design, Automation and Test in Europe
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Disjunctive interpolants for horn-clause verification
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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The problem of computing Craig interpolants has recently received a lot of interest. In this article, we address the problem of efficient generation of interpolants for some important fragments of first-order logic, which are amenable for effective decision procedures, called satisfiability modulo theory (SMT) solvers. We make the following contributions. First, we provide interpolation procedures for several basic theories of interest: the theories of linear arithmetic over the rationals, difference logic over rationals and integers, and UTVPI over rationals and integers. Second, we define a novel approach to interpolate combinations of theories that applies to the delayed theory combination approach. Efficiency is ensured by the fact that the proposed interpolation algorithms extend state-of-the-art algorithms for satisfiability modulo theories. Our experimental evaluation shows that the MathSAT SMT solver can produce interpolants with minor overhead in search, and much more efficiently than other competitor solvers.