Of course, converting NFA to DFA is not a problem. But what about the other direction?
My motivation is the notion of minimization regular expressions using the DFA minimization algorithm.
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You should have asked first what you wanted : your second line. Why assume that you have to reverse the determinization procedure to get back to a regular expression. You confused your readers. You might add it as a possible way you imagined to go about it, after you stated what you want, not before.
To find out how to get a RE from a FA, just search the web for : "convert finite automata to regular expressions". It is an interesting topic.
If you want a "minimal regular expression", just search for that. But I am not sure what minimal would mean (number of operators used ?).
If you want to find a "minimal NFA" search for that, but I gather it is a rather difficult problem, still under research.
If you want a "minimal DFA", search for that. It is a well explored problem.