Theory of linear and integer programming
Theory of linear and integer programming
Asymptotically fast computation of Hermite normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Presburger''s Article on Integer Arithmetic: Remarks and Translation
Presburger''s Article on Integer Arithmetic: Remarks and Translation
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
Encoding RTL Constructs for MathSAT: a Preliminary Report
Electronic Notes in Theoretical Computer Science (ENTCS)
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 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
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
Efficient generation of craig interpolants in satisfiability modulo theories
ACM Transactions on Computational Logic (TOCL)
Solving recursion-free horn clauses over LI+UIF
APLAS'11 Proceedings of the 9th Asian conference on Programming Languages and 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 also present an interpolation result for conjunctions of mixed integer linear equations. We show the utility of the proposed interpolation algorithms for discovering modular/divisibility predicates 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.