Effect of operators on straight line complexity

Abstract

This paper concerns lower bounds on the straight line complexity of multi-variate polynomials. We obtain a conditional result showing that certain explicit linear operators must greatly increase the complexity of some polynomials. We do so by showing that if these operators roughly preserve the complexity of all polynomials then, co-NP is in AM. We show that certain explicit operators must vastly increase the straight line complexity of certain polynomials.