I've run into a problem where I have a set of inputs, as well as a couple known input-output pairs. I am interested in the output, but in order to get that, I need to figure out how the input is used to generate the output.
So for example, I might have the following input strings along with a few known output strings
char001 --> dasjudash2 // known input/output char002 --> ef2y789e2y // known char003 --> jnjxf9823d // known char004 --> ? // unknown output char005 --> ? // unknown output
I believe that there may exist some algorithm that takes an input and produces the given output, but this algorithm is unknown. It is very possible that the pairs are randomly generated as well (eg: look at the sky, randomly pick a string of characters). I could stare at it long and hard and try to think of how they are related, but computers can probably help me out.
Basically, given known inputs and outputs, is it possible to come up with potential functions that will take known inputs and generate known outputs, and then use that to take the rest of the inputs and generate the corresponding outputs?
Given that the solution may be one of an infinite possibilities (including the possibility that no solution exists, in the case that someone did just look at the sky and pick random characters out of a hat), I would quickly dismiss it as a computationally infeasible task, but perhaps my intuition is wrong and there is research evidence to show that this problem is solvable?