# Circuits computing functions of inputs smaller than $n$

The usual circuit complexity concerns circuits where circuit $C_n$ computes function $f_n$. I am interested in circuits such that $C_n$ can compute $f_i$ for all $i \leq n$. I am assuming that the first $\log n$ inputs specify the $i$.

• I believe so. At the same time, I do not think there is a general construction with better polynomial, since the functions may be completely different for different $n$'s. Not sure about uniform circuit classes, though. Perhaps there is better polynomial for them? – user2316602 Jun 11 '18 at 16:10