Back in Nand Land

Stopped for a while on QM, its either the work of a genius or a madman, and I don't really feel like thinking about it anymore. There are a lot of fuzzy conclusions even after looking at it for a short while, it works, but the interpretations of it and derived theorems sometimes are a mess.

A question I've been wondering about deals with minimal Nand terms. It is trivial to enumerate them. The simplest is just start of with a fixed number of variables, call that set S0, then S1 is the set of all combinations up to isomorphism of S0, and S2 the set of all combinations of S0 and S1, etc.

Now of course that leads to a numbering on terms, that is if you consider a set to be a vector for a moment. A minimization strategy is a function mapping a number on a number of terms which encode the same state space. Note that calculating a specific number for any given term by a computer would be prohibitive, since a term encodes a function out of 2**(2**n), and a term will have a number at least as big. Question is, can you do without the number, and what is the mapping which relates terms by trivial rewrites, and also, the in-degree and out-degree of terms? And also, what are the trajectories in Sx, how far, if anything, do you go up or down in x?

P!=NP says there is no trivial strategy, or trivial strategies are of exponential length, but still, you can study the relationships and 'possible' confluent functions. With a big computer, it gives an empirical study of the question.

The interesting thing is, if PRIME would correspond to a polynomial deterministic minimization, why wouldn't FACTOR?

Its been years since I was interested in this, seems I forgot a lot. Some terms have polynomial rewrite strategies, should look it up again.


Armchair programming and loose thinking.