Logic for computer science: foundations of automatic theorem proving
Logic for computer science: foundations of automatic theorem proving
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
ICS: Integrated Canonizer and Solver
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Electronic Notes in Theoretical Computer Science (ENTCS)
Efficient Craig Interpolation for Linear Diophantine (Dis)Equations and Linear Modular Equations
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
Interpolation and Symbol Elimination
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Constraint solving for interpolation
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
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
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
Efficient generation of craig interpolants in satisfiability modulo theories
ACM Transactions on Computational Logic (TOCL)
Constraint solving for interpolation
Journal of Symbolic Computation
Beyond quantifier-free interpolation in extensions of Presburger arithmetic
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
An interpolating decision procedure for transitive relations with uninterpreted functions
HVC'09 Proceedings of the 5th international Haifa verification conference on Hardware and software: verification and testing
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
On interpolation in decision procedures
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Craig interpolation in the presence of non-linear constraints
FORMATS'11 Proceedings of the 9th international conference on Formal modeling and analysis of timed systems
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Zap: automated theorem proving for software analysis
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Flexible interpolation with local proof transformations
Proceedings of the International Conference on Computer-Aided Design
Interpolation in local theory extensions
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Propositional interpolation and abstract interpretation
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
Interpolation and symbol elimination in vampire
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Solving recursion-free horn clauses over LI+UIF
APLAS'11 Proceedings of the 9th Asian conference on Programming Languages and Systems
Interpolant strength revisited
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
From strong amalgamability to modularity of quantifier-free interpolation
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
When boolean satisfiability meets gaussian elimination in a simplex way
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
SMTInterpol: an interpolating SMT solver
SPIN'12 Proceedings of the 19th international conference on Model Checking Software
Complete instantiation-based interpolation
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proof tree preserving interpolation
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Quantifier-free interpolation in combinations of equality interpolating theories
ACM Transactions on Computational Logic (TOCL)
Generating non-linear interpolants by semidefinite programming
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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We present a combination method for generating interpolants for a class of first-order theories. Using interpolant-generation procedures for individual theories as black-boxes, our method modularly generates interpolants for the combined theory. Our combination method applies for a broad class of first-order theories, which we characterize as equality-interpolating Nelson-Oppen theories. This class includes many useful theories such as the quantifier-free theories of uninterpreted functions, linear inequalities over reals, and Lisp structures. The combination method can be implemented within existing Nelson-Oppen-style decision procedures (such as Simplify, Verifun, ICS, CVC-Lite, and Zap).