What I would like to do is design a program (for academic purposes) which will take a representation of a DFA (as a directed graph) and display the regular language which it accepts, in a reasonable format.
For this graph: as input, an algorithm will spit out:
The set of regular languages is computable and decidable. But what about the language which we use to represent regular languages? Is it decidable as well?
Edit: I thought about this some more, and I think this should be doable, because implementation examples of regular expression parsers are bountiful, and clearly they internally construct a graph (or an equivalent structure). What I am wondering is if the reverse is possible -- construct the correct expression from a DFA representation.