We revisit the main result of Carmosino et al \cite{CILM18} which shows that an $\Omega(n^{\omega/2+\epsilon})$ size noncommutative arithmetic circuit size lower bound (where $\omega$ is the matrix multiplication exponent) for a constant-degree $n$-variate polynomial family $(g_n)_n$, where each $g_n$ is a noncommutative polynomial, can be ``lifted'' to an exponential size circuit size lower bound for another polynomial family $(f_n)$ obtained from $(g_n)$ by a lifting process. In this paper, we present a simpler and more conceptual automata-theoretic proof of their result.

翻译：我们重新审视Carmosino等人\cite{CILM18}的主要结果，该结果表明：对于常次数n元多项式族(g_n)_n（其中每个g_n均为非交换多项式），若其非交换算术电路规模下界为Ω(n^{ω/2+ε})（其中ω为矩阵乘法指数），则可通过提升过程从(g_n)构造另一多项式族(f_n)，并得到指数级电路规模下界。本文提出了一种更简洁、更具概念性的自动机理论证明方法。