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## Affiliation:

University of New Mexico

Department of Computer Science

Albuquerque, NM 87131

United States of America

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Abstract: An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities can be linearized if they are concave. A generalization of Motzkin's transposition theorem is proved, which is used to generate an interpolant between two mutually contradictory conjunctions of polynomial inequalities, in a way similar to the linear inequalities case. This can be done efficiently using semi-definite programming but forsaking completeness. A combination algorithm is given for the combined theory of concave quadratic polynomial inequalities and the equality theory over uninterpreted functions symbols using a hierarchical framework for combining interpolation algorithms for quantifier-free theories. A preliminary implementation has been explored.