How familiar are you with this area? I think that this sort of thing is already well-studied, but I have only vague memories to go by.
As an aside, you only need (AND and NOT) or (OR and NOT), not all three; and if you have NAND or NOR, either of those is sufficient by itself.
I'm a computer expert but a brain newbie.
The typical CPU is built from n-NOR, n-NAND, and NOT gates. The NOT gates works like a 1-NAND or a 1-NOR (they're the same thing, electronically). Everything else, including AND and OR, are made from those three. The actual logic only requires NOT and {1 of AND, OR, NAND, NOR}. Notice there are several sets of minimum gates and and a larger set of used gates.
The brain (I'm theorizing now, I have no background in neural chemistry) has a similar set of basic gates that can be organized into a Turing machine, and the gate I described previously is one of them.
Previous Open Thread: http://lesswrong.com/r/discussion/lw/k9x/open_thread_may_26_june_1_2014/
(oops, we missed a day!)
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