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The probability of “undefined” (non-converging) output in generating the universal probability distribution

Solomonoff, Ray J.

Information processing letters, 2008-06, Vol.106 (6), p.238-240 [Periódico revisado por pares]

Amsterdam: Elsevier B.V

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Título:
The probability of “undefined” (non-converging) output in generating the universal probability distribution
Autor: Solomonoff, Ray J.
Assuntos: Algorithmic probability ; Algorithmics. Computability. Computer arithmetics ; Algorithms ; Analysis of algorithms ; Applied sciences ; Automata. Abstract machines. Turing machines ; Complexity theory ; Computer science; control theory; systems ; Exact sciences and technology ; Halting problem ; Incomputable ; Kolmogorov complexity ; Miscellaneous ; Normalization ; Probability ; Probability distribution ; Studies ; Theoretical computing ; Theory of computation ; Turing machine ; Universal probability distribution ; Universal Turing machine
É parte de: Information processing letters, 2008-06, Vol.106 (6), p.238-240
Descrição: In order to generate a universal probability distribution to extrapolate a binary string x of length i, we feed random bits into a universal device, M. When we find an input string that gives an output matching x, we continue the successful input with random bits until M produces a zero or one as output. The relative probabilities of these two continuations can give a normalized prediction for the probability of the symbol following x. There is, however, a probability, P i + 1 ( u ) that the continued random input string will not generate any output for the ( i + 1 ) th symbol. We will show E μ ∑ i = 1 n P i ( u ) ⩽ k μ ln 2 . Here E μ is the expected value with respect to μ, the probability distribution that created x. k μ is the Kolmogorov complexity of μ with respect to M. n is any positive integer. Usually we do not know μ and so we do not know k μ . However, if μ is the uniform distribution, we can usually find a good upper bound for k μ .
Editor: Amsterdam: Elsevier B.V
Idioma: Inglês

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The probability of “undefined” (non-converging) output in generating the universal probability distribution

Solomonoff, Ray J.

Amsterdam: Elsevier B.V

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