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

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, Pi+1(u) that the continued random input string will not generate any output for the i + 1th symbol. We will show E

• Type: Journal
• Year: 2008
• Where: IPL
• Authors: Ray J. Solomonoff
• Keywords: Input String, IPL 2008, Probability Distribution, Random Bits