P not equal NP - because hopfield/boltzmann energy function is intractable
P not equal NP - because hopfield/boltzmann energy function is intractable
About the legal issues of creating and distributing encryption software, my position is that optimizations of NPComplete in general are not encryption software for the same reason the rules of chess are not a specific board setup you may arrive at later, which for some reason, it may be illegal to export chess games where the king makes it all the way to the opposite row, for example. Its true that every computer can perform encryption, but a computer by itself is not encryption.
On the other hand, if
Visual Integer Factor was hooked to a good enough NPComplete optimization, layering the "game board" 1 taller per compute cycle, some people may say factoring variable size binary integers (if it worked, and since P not equal NP I'm not sure how intractable it may be, but integer factoring appears exponential but still less than NPComplete) is most useful for trying to decrypt RSA without having the key (some may say if it went that way), but there is also the more basic purpose of completing what we learn in elementary school, the inverse of multiply being factor (because, whats the divide of 15? makes no sense without multiple parameters), so I would at least stand by it as an educational tool for factoring small binary integers visually (click on screen drag the bits around, it already does), and if anyone has a problem with software to teach and calculate elementary level math (multiply/factor) then let the book burning begin, and when there are no more multiplies around, then we'll have no need for multiplying in reverse (its inverse). The issue is not any software's possible connection to encryption; The issue is reversing time. NAND goes forward as a Recognizer function, but backward it generates possible pasts, what you could have put in to get a positive or negative recognize (or however many bits, 1 forest root each). The issue is peoples clock said an earlier time when the output was first generated and then again in the future if some software could optimize NPComplete or even integer factoring well enough. The past is thought to not be around anymore.
Visual Integer Factor is in the rectangle shape of 2 factors (to be multiplied or just look at them there) when every row and column that has any rectangle/bit on (bright on screen) also has all the others in that row and column on, except between them are blacked out rows and columns where nothing is on, and these can be anywhere it appears. It appears, if you believe it certainly takes exponential time, but what if the energy function (of hopfield/boltzmann described in link below) included a weight for combinations of each row with each column. For example, the highest digit in a row being on would be strongly against the higher digit columns, because its the integer sideways multiplied by the integer vertically, which you should think of like the corner is down, digit weighs half as much everywhere below like in Rule90). The probability of certain rows and columns being blacked out together is whatever covers all possibilities of 2 numbers that could be multiplied to get the single integer asked about its factors. For each digit bigger in one, the other generally goes down 1 digit, and theres probably some subtlety to the combinations of the digits since its a view of pythagorean theorem (a^2 + b^2 = c^2, sum the lengths in digits, square to get the bell curve pascals triangle and rule 90 form into). But this kind of stuff is already known in some combination or another, when the factoring challenge was ended and people thought maybe its good enough. Maybe it is, if the digits of the 2 primes motion-blur in a way that spreads an even bell curve in the digits of the output. Whatever it is, pascals triangle calculates the number of possible paths zigzagging down to each 1 digit (odd number of paths came here) and 0 digit (even number came here). Factoring's strength is that pascals triangle is how bell curves, circles/spheres/hyperspheres and waves are derived from coin flips (technically the binomial distribution, but in the limit). If you cant trust a bell curve to be random, what else is there?