I never studied these specific classes, but my immediate intuition is that an n-input fan-in AND or OR gate can be reduced to a tree of 2-input gates with depth O(log(n)), which preserves polylog complexity, so surely AC = NC.
Wikipedia agrees :)
If you specify the exponent of the log, you get a different answer.
I never studied these specific classes, but my immediate intuition is that an n-input fan-in AND or OR gate can be reduced to a tree of 2-input gates with depth O(log(n)), which preserves polylog complexity, so surely AC = NC.
Wikipedia agrees :)
If you specify the exponent of the log, you get a different answer.
Yes.
There is a beautiful proof of the disjunction between AC0 and NC showing parity cannot be done in AC0 using harmonic analysis of Boolean functions
This one? https://www.cs.huji.ac.il/~nati/PAPERS/lmn.pdf
https://en.wikipedia.org/wiki/Switching_lemma
That paper is in the wiki refs but Hastad’s original is from 1986