Recently, I play a game of Turing completeness where I utilize various gate circuits such as NAND, AND, and NOT to construct a circuit that satisfies the given truth table.
I didn't learn digital circuits or relevant content. When I play this game, I want to know whether there are any theory to deal it. For example, given a truth table, is there any theory to get the circuit with least basic gate (or only Nand gate). It seems to be a bit like graph theory (but the vertices are special).
On the other hand, I know a little about retina from From Neuron to Brain. The retina responds to certain shapes of light, such as a ring of light. I've always wondered how build a neural network with neurons that respond to ring of light but not solid circle light.
Of course, I'm not really asking for the details of these questions. I just feel they may are the thing not liking analysis and algebra. If I want to deal these questions, what book I should begin from ?