Assume that we have an unbounded fan-in circuit family of depth $d(n)$ and size $s(n)$. What is the smallest depth (in terms of $d(n)$ and $n$ and $s(n)$) bounded fan-in circuit family of size $poly(s)$ for it?In particular what is the largest depth $d(n)$ for which we know polynomial size unbounded fan-in circuit families of depth $d(n)$ are in $\mathsf{NC^1}$?
Depth of bounded fan-in circuits for unbounded fan-in circuits
cc.complexity theory;reference request;circuit complexity;circuit depth