If I understand your question correctly, it boils down to asking how long is a minimal implementation of the AIXItl algorithm. The answer to that is, pretty short; it would fit in one page of code. (This fact is of little practical importance, of course, since it would still require much more computation than is possible according to our current understanding of physics.)
It’s possible I’m not understanding your question correctly, in which case please point out what I’m missing.
K(AIXItl) ⇐ length of code that Hutter actually took to write it ~ 300 lines of code.
With respect to a minimal state-symbol turing machine it would be 300 + (however much it takes to translate common math concepts like “argmax” into the minimal state-symbol turing machine’s language).
I think that’s the question, unless there are some shorter or in some way better computable approximations to AIXI out there. I am not as familiar with this field as I would like, so someone please correct me if I’m making a silly mistake somewhere.
If anyone has gone to the trouble of actually counting the number of bits in AIXItl (in some particular, simple programming language / UTM), that would be nice to quote.
One variant somebody actually implemented is called Monte Carlo AIXI; granted that it won’t have been optimized for minimum code size, but a Google search might find you a copy of the code you could download and look at its size for an upper bound.
If I understand your question correctly, it boils down to asking how long is a minimal implementation of the AIXItl algorithm. The answer to that is, pretty short; it would fit in one page of code. (This fact is of little practical importance, of course, since it would still require much more computation than is possible according to our current understanding of physics.)
It’s possible I’m not understanding your question correctly, in which case please point out what I’m missing.
I agree with this.
K(AIXItl) ⇐ length of code that Hutter actually took to write it ~ 300 lines of code.
With respect to a minimal state-symbol turing machine it would be 300 + (however much it takes to translate common math concepts like “argmax” into the minimal state-symbol turing machine’s language).
I think that’s the question, unless there are some shorter or in some way better computable approximations to AIXI out there. I am not as familiar with this field as I would like, so someone please correct me if I’m making a silly mistake somewhere.
If anyone has gone to the trouble of actually counting the number of bits in AIXItl (in some particular, simple programming language / UTM), that would be nice to quote.
One variant somebody actually implemented is called Monte Carlo AIXI; granted that it won’t have been optimized for minimum code size, but a Google search might find you a copy of the code you could download and look at its size for an upper bound.