in reply to Testing regex equivalence
The short answer is that you can do this by converting regular expressions to NFAs/DFAs (for more details, see my reply in the thread I referenced). However, this cannot be done in a super-efficient way. In fact, the problem of deciding equivalence of two regular expressions is PSPACE-complete (which is bad ;)). Even in your special case of deciding whether a regular expression accepts all strings, the problem remains PSPACE-complete (google for regular expression universality).
Being PSPACE-complete does not mean it's impossible. It's quite possible, but will quickly become very impractical for large regular expressions..
As for how to do the conversion to NFA/DFA, I can tell you that another monk and I are working on a formal language & automata toolkit that will make this easy, but it won't be ready for a while...
Update: as for your idea above to "simplify" a regex, that is essentially the same thing and will not gain you anything. Testing regex equivalency reduces to the problem of finding the "simplest" equivalent regex (no matter how you define "simplest"), so regex simplification is still a PSPACE-hard problem (-hard instead of -complete because we're now talking about a search procedure, not a decision procedure).