I have N strings. Also, there are K regular expressions, unknown to me. Each string is either matching one of the regular expressions, or it is garbage. There are total of
What you are trying to do is language learning or language inference with a twist: instead of generalising over a set of given examples (and possibly counter-examples), you wish to infer a language with a small yet specific grammar.
I'm not sure how much research is being done on that. However, if you are also interested in finding the minimal (= general) regular expression that accepts all n strings, search for papers on MDL (Minimum Description Length) and FSMs (Finite State Machines).
Two interesting queries at Google Scholar: