Generating non-linear interpolants by semidefinite programming

Authors:
Liyun Dai;Bican Xia;Naijun Zhan
Affiliations:
LMAM & School of Mathematical Sciences, Peking University, China,Beijing International Center for Mathematical Research, Peking University, China;LMAM & School of Mathematical Sciences, Peking University, China;State Key Laboratory of Computer Science, Institute of Software, CAS, China
Venue:
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Year:
2013

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Abstract

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model checking, CEGAR, SMT, etc., in which the hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, little work focuses on discovering polynomial interpolants in the literature. In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.