Foundations of Induction - of Marcus Hutter

More documents

Recommendations

Info

Marcus Hutter - 22 - Foundations of InductionTuring Machines & Effective Enumeration• Turing machine (TM) = (mathematicalmodel for an) idealized computer.• See e.g. textbook [HMU06]Show Turing Machine in Action: TuringBeispielAnimated.gif• Instruction i: If symbol on tapeunder head is 0/1, write 0/1/-and move head left/right/notand goto instruction=state j.• {partial recursive functions }≡ {functions computable with a TM}.• A set of objects S = {o 1 , o 2 , o 3 , ...} can be (effectively) enumerated:⇐⇒ ∃ TM machine mapping i to ⟨o i ⟩,where ⟨⟩ is some (often omitted) default coding of elements in S.
Marcus Hutter - 23 - Foundations of InductionInformation Theory & Kolmogorov Complexity• Quantification/interpretation of Occam’s razor:• Shortest description of object is best explanation.• Shortest program for a string on a Turing machineT leads to best extrapolation=prediction.K T (x) = minp{l(p) : T (p) = x}• Prediction is best for a natural universal Turing machine U.Kolmogorov-complexity(x) = K(x) = K U (x)≤ K T (x) + c T
Page 1 and 2: Foundations of InductionMarcus Hutt
Page 4: Marcus Hutter - 4 - Foundations of
Page 15 and 16: Marcus Hutter - 15 - Foundations of

Foundations of Induction - of Marcus Hutter

Create successful ePaper yourself

Delete template?

Save as template?