  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.
