Can probabilistic Turing machines be considered a generalization of deterministic Turing machines, so that DTMs can be described in terms of PTMs?
Editing in reply to your edit: I thought Solomonoff Induction was made for a purpose. Quoting from Legg's paper:
Solomonoff's induction method is an attempt to design a general all purpose inductive inference system. Ideally such a system would be able to accurately learn any meaningful hypothesis from a bare minimum of appropriately format- ted information.
I'm just pointing out what I see as a limitation in the domain of problems classical Solomonoff Induction can successfully model.
Can probabilistic Turing machines be considered a generalization of deterministic Turing machines, so that DTMs can be described in terms of PTMs?
Yes.
I'm just pointing out what I see as a limitation in the domain of problems classical Solomonoff Induction can successfully model.
I don't think anyone claims that this limitation doesn't exist (and anyone who claims this is wrong). But if your concern is with actual coins in the real world, I suppose the hope is that AIXI would eventually learn enough about physics to just correctly predict the outcome of coin flips.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Of course, for "every Monday", the last one should have been dated July 22-28. *cough*