Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 beten two mutually contradictory conjunctions of polynomial inequalities, using semi-definite programming in time complexity $$\mathcal {O}n^3+nm$$, where n is the number of variables and m is the number of inequalities This complexity analysis assumes that despite the numerical nature of approximate SDP algorithms, they are able to generate correct ansrs in a fixed number of calls.. Using the framework proposed in [22] for combining interpolants for a combination of quantifier-free theories which have their own interpolation algorithms, a combination algorithm is given for the combined theory of concave quadratic polynomial inequalities and the equality theory over uninterpreted functions EUF.
['Ting Gan', 'Liyun Dai', 'Bican Xia', 'Naijun Zhan', 'Deepak Kapur', 'Mingshuai Chen']
I am writing a research paper on a idea Interpolant Synthesis for Quadratic Polynomial Inequalities and Combination with EUF
[{"from": "human", "value": "I am writing a research paper on a idea Interpolant Synthesis for Quadratic Polynomial Inequalities and Combination with EUF"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 beten two mutually contradictory conjunctions of polynomial inequalities, using semi-definite programming in time complexity $$\\mathcal {O}n^3+nm$$, where n is the number of variables and m is the number of inequalities This complexity analysis assumes that despite the numerical nature of approximate SDP algorithms, they are able to generate correct ansrs in a fixed number of calls.. Using the framework proposed in [22] for combining interpolants for a combination of quantifier-free theories which have their own interpolation algorithms, a combination algorithm is given for the combined theory of concave quadratic polynomial inequalities and the equality theory over uninterpreted functions EUF."}]