Introduction to Algorithms
The software model checker Blast: Applications to software engineering
International Journal on Software Tools for Technology Transfer (STTT)
Efficient Craig Interpolation for Linear Diophantine (Dis)Equations and Linear Modular Equations
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Constraint solving for interpolation
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Applications of craig interpolants in model checking
TACAS'05 Proceedings of the 11th 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
Efficient generation of craig interpolants in satisfiability modulo theories
ACM Transactions on Computational Logic (TOCL)
Constraint solving for interpolation
Journal of Symbolic Computation
Interpolating quantifier-free Presburger arithmetic
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
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
An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic
Journal of Automated Reasoning
An interpolating sequent calculus for quantifier-free presburger arithmetic
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
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The linear arithmetic solver in Yices was specifically designed for SMT provers, providing fast support for operations like adding and deleting constraints. We give a procedure for developing interpolants based on the results of the Yices arithmetic solver. For inequalities over real numbers, the interpolant is computed directly from the one contradictory equation and associated bounds. For integer inequalities, a formula is computed from the contradictory equation, the bounds, and the Gomory cuts. The formula is not exactly an interpolant because it may contain local variables. But local variables only arise from Gomory cuts, so there will not be many local variables, and the formula should thereby be useful for applications like predicate abstraction. For integer equalities, we designed a new procedure. It accepts equations and congruence equations, and returns an interpolant. We have implemented our method and give experimental results.