solipsist comments on Computable Universal Prior - Less Wrong

0 Post author: potato 11 December 2015 09:54AM

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Comment author: solipsist 12 December 2015 01:06:29AM *  3 points [-]

Spit balling hacks around this:

  • Weigh hypotheses based on how many steps it takes for them to be computed on a dovetailing of all Turing machines. This would probably put too much weight on programs that are large but fast to compute.

  • Weigh hypotheses on how much space it takes to compute them. So dovetail all turing machines of size up to n limited to n bits of space for at most 2^n steps. This has the nice property that the prior is, like the hypotheses, space limited (using about twice as much space as the hypothesis).

  • Find some quantum algorithm that uses n^k qubits and polynomial time to magically evaluate all programs of length of n in some semi-reasonable way. If such a beast exists (which I doubt), it has the nice property that it "considers" all reasonably sized hypotheses yet runs in polynomial space and time.

  • Given n bits of evidence about the universe, consider all programs of length up to k*log(n) run for at most n^k2 steps. This has the nice property that it runs in polynomial time and space.