How to determine if a regex is orthogonal to another regex?

Question

I guess my question is best explained with an (simplified) example.

Regex 1:

^\\d+_[a-z]+$

Regex 2:

^\\d*$
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Answer 1

I finally found exactly the library that I was looking for:

dk.brics.automaton

Usage:

/**
 * @return true if the two regexes will never both match a given string
 */
public boolean isRegexOrthogonal( String regex1, String regex2 ) {
   Automaton automaton1 = new RegExp(regex1).toAutomaton();
   Automaton automaton2 = new RegExp(regex2).toAutomaton();
   return automaton1.intersection(automaton2).isEmpty();
}

It should be noted that the implementation doesn't and can't support complex RegEx features like back references. See the blog post "A Faster Java Regex Package" which introduces dk.brics.automaton.