Recently, I've been studying neural networks to get a better understanding of how they work. I can't help but notice a vague similarity to K-Maps or Karnaugh Maps used for determining boolean functions between inputs and outputs.
When I studied K-maps, I once had a naive and vague idea that it might be possible to decipher an algebraic formula from a pattern of numbers by applying a K-map. For instance, the input would be 1,2,3,4 and the output would be 2,4,6,8 and the K-Map would yield 2x. I figured if the K-Map operations used fuzzy logic instead of simple boolean logic, it might be possible. It seemed to silly to even consider it further.
After reading about neural networks, however, and how the inputs and outputs are processed through a network of operations, it makes me wonder if this may be influenced by K-maps. Both have similar constraint where accuracy is dependent on the size of its input. They do differ, however, in their respective artifacts. A K-map yield an independent function, whereas a Neural Network becomes the function itself.
Is there any influence between the two historically? Is there any similarities between the two? I came across an interesting research, but being a layman, it was way over my head:
Not really.
K-maps define/describe a particular boolean function by showing the output for all possible inputs, but how that function is actually computed/implemented in terms of elementary operations like 'and', 'or', or 'not' is not specified.
Neural networks can be used to compute functions ... rather than describe their overall input-output behavior. And those functions can be just about any function, so not necessarily any boolean ones.
I suppose you could try and use a neural network to compute a boolean function as defined by a K-map ... though I see really little practical value in that when classical circuits can do the same thing ... it's overkill in a way to try and use a neural network.
I took a look at the paper you linked ... it's very poorly written, and in the end really not clear what it is proposing ... it seems the author is trying to use a neural network not to implement a boolean function, but rather to do the creation of groups in order to reduce/simplify a boolean circuit. What exactly that algorithm is and how that works is not clear though ... maybe this was just a 1-page summary of a much longer paper? Regardless, there is nothing about this paper that would suggest any kind of historical connection between K-maps and neural networks.