Reasoning About Recursively Defined Data Structures
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Model-Theoretic Methods in Combined Constraint Satisfiability
Journal of Automated Reasoning
An interpolating theorem prover
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
Interpolation for data structures
Proceedings of the 14th ACM SIGSOFT international symposium on Foundations of software engineering
CSIsat: Interpolation for LA+EUF
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
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,
Finding Loop Invariants for Programs over Arrays Using a Theorem Prover
FASE '09 Proceedings of the 12th International Conference on Fundamental Approaches to Software Engineering: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
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
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
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
On interpolation in decision procedures
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Interpolation in local theory extensions
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Applications of craig interpolation to model checking
ICATPN'05 Proceedings of the 26th international conference on Applications and Theory of Petri Nets
Efficient satisfiability modulo theories via delayed theory combination
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
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
An interpolating sequent calculus for quantifier-free presburger arithmetic
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
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
Lazy abstraction with interpolants for arrays
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
SAFARI: SMT-based abstraction for arrays with interpolants
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
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The use of interpolants in verification is gaining more and more importance. Since theories used in applications are usually obtained as (disjoint) combinations of simpler theories, it is important to modularly reuse interpolation algorithms for the component theories. We show that a sufficient and necessary condition to do this for quantifier-free interpolation is that the component theories have the strong (sub-)amalgamation property. Then, we provide an equivalent syntactic characterization and show that such characterization covers most theories commonly employed in verification. Finally, we design a combined quantifier-free interpolation algorithm capable of handling both convex and nonconvex theories; this algorithm subsumes and extends most existing work on combined interpolation.