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71 points by amichail 4 days ago | 6 comments

This is an awesome result.

For those unfamiliar: NC is the class of problems which can be solved in polylogarthmic depth with polynomial number of logic gates. It is unproven if NC != P similar to P != NP.

osti 3 minutes ago

So is it a class of problems that can be parallelized well?

gignico 2 hours ago

Yes, but logic gates with constant fan-in, crucially, otherwise that's called AC.

amluto 13 minutes ago

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.

amirhirsch 60 minutes ago

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

vintermann 2 hours ago

Many years ago, on Boardgamegeek, there was a game trading system called "Math Trades", where participants would list a number of trades they were willing to make, and they ran some complicated calculations to figure out how to let as many as possible trade.

CS professor Chris Okasaki, known for his book on purely functional data structures, also played board games and he came across this phenomenon. He realized that it could be modelled as a bipartite matching problem, and wrote a MUCH faster program to manage math trades.

https://okasaki.blogspot.com/2008/03/what-heck-is-math-trade...

I guess it can be made even faster now in theory.

kevinten10 3 hours ago

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