Generating non-linear interpolants by semidefinite programming

Interpolation-based techniques have been widely and successfully ap-plied in the verification of hardware and software, e.g., in bounded-model check-ing, CEGAR, SMT, etc., in which the hardest part is how to synthesize inter-polants. 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 lit-erature. In this paper, we provide an approach for constructing non-linear inter-polants based on semidefinite programming, and show how to apply such results to the verification of programs by examples