Interpolants for Linear Arithmetic in SMT

  • Christopher Lynch
  • Yuefeng Tang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5311)


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.


Free Variable Active Bound Predicate Abstraction Linear Arithmetic Extension Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Christopher Lynch
    • 1
  • Yuefeng Tang
    • 1
  1. 1.Department of Mathematics and Computer ScienceClarkson UniversityPotsdamUSA

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