Which $AC^0$ problems are not "truly feasible"? Neil Immerman's famous Picture of The World is the following (click to enlarge):

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His "Truly feasible" class includes no other class; my question is then:


  What is an AC0 problem which is considered to be unpractical, and why?
If you want an example of an AC0 function that requires depth $d$, and cannot be computed by AC0 circuits of depth $d-1$, then try the Sipser functions $S^{d,n}$. The superscript $d$ is depth needed for a polynomial-size AC0 circuit. With depth $d-1$, the circuit would need exponentially many gates.

So computing $S^{d,n}$ for $d = 10^{10^{100}}$ would not be "truly feasible."

EDIT: Your question also asks why this would not be feasible. I guess the reason is that $10^{10^{100}}$ is more than the number of atoms in the visible universe.