Closure of VP under taking factors: a short and simple proof

Chi-Ning Chou; Mrinal Kumar; Noam Solomon

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arXiv · 1903.02366

Closure of VP under taking factors: a short and simple proof

Chi-Ning Chou·Mrinal Kumar·Noam Solomon

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Abstract

In this note, we give a short, simple and almost completely self contained proof of a classical result of Kaltofen [Kal86, Kal87, Kal89] which shows that if an $n$ variate degree $d$ polynomial $f$ can be computed by an arithmetic circuit of size $s$, then each of its factors can be computed by an arithmetic circuit of size at most $\textsf{poly}\left(s, n, d\right)$. However, unlike Kaltofen's argument, our proof does not directly give an efficient algorithm for computing the circuits for the factors of $f$.

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Chi-Ning Chou, Mrinal Kumar, Noam Solomon. 2019-03-06. Closure of VP under taking factors: a short and simple proof. https://arxiv.org/abs/1903.02366

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