Sharper and Simpler Nonlinear Interpolants for Program Verification

Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al. that combines real algebraic geometry and SDP optimization in synthesis of polynomial interpolants, the...

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Bibliographic Details
Published inProgramming Languages and Systems Vol. 10695; pp. 491 - 513
Main Authors Okudono, Takamasa, Nishida, Yuki, Kojima, Kensuke, Suenaga, Kohei, Kido, Kengo, Hasuo, Ichiro
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2017
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Interpolation
Nonlinear interpolant
Numerical optimization
Polynomial
Program verification
Real algebraic geometry
SDP optimization
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Summary:Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al. that combines real algebraic geometry and SDP optimization in synthesis of polynomial interpolants, the current paper contributes its enhancement that yields sharper and simpler interpolants. The enhancement is made possible by: theoretical observations in real algebraic geometry; and our continued fraction-based algorithm that rounds off (potentially erroneous) numerical solutions of SDP solvers. Experiment results support our tool’s effectiandveness; we also demonstrate the benefit of sharp and simple interpolants in program verification examples.
ISBN:3319712365
9783319712369
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-319-71237-6_24