In this work we consider representations of multivariate polynomials in $F[x]$ of the form $ f(x) = Q_1(x)^{e_1} + Q_2(x)^{e_2} + ... + Q_s(x)^{e_s},$ where the $e_i$'s are positive integers and the $Q_i$'s are arbitary multivariate polynomials of bounded degree. We give an explicit $n$-variate polynomial $f$ of degree $n$ ... more >>>

Arithmetic complexity, the study of the cost of computing polynomials via additions and multiplications, is considered (for many good reasons) simpler to understand than Boolean complexity, namely computing Boolean functions via logical gates. And indeed, we seem to have significantly more lower bound techniques and results in arithmetic complexity than ... more >>>