The shortest theory among those that best explains all observations from past observations, for all observations and past observations (= Solomonoff induction). (Since I don't have a theory that provably explains all observations, I have to use proof candidates, unfortunately.)
As far as I understand, the set of functions computable by a reasonably resource bounded QTM is different from a resource bounded TM?
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If you run your TM to infinity then it can do amazing things, of course, but we are talking about mappings from finite int to finite int vs. real to real, or real to complex to complex to real.
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