Theory of linear and integer programming
Theory of linear and integer programming
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Counterexample-guided abstraction refinement for symbolic model checking
Journal of the ACM (JACM)
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Interpolation for data structures
Proceedings of the 14th ACM SIGSOFT international symposium on Foundations of software engineering
Analysis of modular arithmetic
ACM Transactions on Programming Languages and Systems (TOPLAS) - Special Issue ESOP'05
Lifting Propositional Interpolants to the Word-Level
FMCAD '07 Proceedings of the Formal Methods in Computer Aided Design
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
A combination method for generating interpolants
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
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
Interpolants for Linear Arithmetic in SMT
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Cuts from Proofs: A Complete and Practical Technique for Solving Linear Inequalities over Integers
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Interpolant Generation for UTVPI
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Interpolating quantifier-free Presburger arithmetic
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
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
A quantifier elimination algorithm for linear modular equations and disequations
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Cuts from proofs: a complete and practical technique for solving linear inequalities over integers
Formal Methods in System Design
An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic
Journal of Automated Reasoning
MERIT: an interpolating model-checker
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Effective word-level interpolation for software verification
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
Extending quantifier elimination to linear inequalities on bit-vectors
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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The use of Craig interpolants has enabled the development of powerful hardware and software model checking techniques. Efficient algorithms are known for computing interpolants in rational and real linear arithmetic. We focus on subsets of integer linear arithmetic. Our main results are polynomial time algorithms for obtaining interpolants for conjunctions of linear diophantine equations, linear modular equations (linear congruences), and linear diophantine disequations. We show the utility of the proposed interpolation algorithms for discovering modular/divisibilitypredicates in a counterexample guided abstraction refinement (CEGAR) framework. This has enabled verification of simple programs that cannot be checked using existing CEGAR based model checkers.