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Submitted 1996. [90] G. t’Hooft. Quantum gravity as a dissipative deterministic system. gov/abs/gr-qc/9903084, Institute for Theoretical Physics, Univ. of Utrecht, and Spinoza Institute, Netherlands, 1999. Also published in Classical and Quantum Gravity 16, 3263. [91] T. Toffoli. The role of the observer in uniform systems. In G. Klir, editor, Applied General Systems Research. Plenum Press, New York, London, 1978. [92] A. M. Turing. On computable numbers, with an application to the Entscheidungsproblem.

Compare [56, p. 282 ff]. Solomonoff showed that the µM -probability of a particular continuation converges towards µ as the observation size goes to infinity [83]. Hutter recently extended his results by showing that the number of prediction errors made by universal Solomonoff prediction is essentially bounded by the number of errors made by any other recursive prediction scheme, including the optimal scheme based on the true distribution µ [47]. Hutter also extended Solomonoff’s passive universal induction framework to the case of agents actively interacting with an unknown environment [49].

Sc. Thesis, Dept. , 1949. [52] L. A. Levin. On the notion of a random sequence. Soviet Math. , 14(5):1413–1416, 1973. [53] L. A. Levin. Universal sequential search problems. Problems of Information Transmission, 9(3):265–266, 1973. 46 [54] L. A. Levin. Laws of information (nongrowth) and aspects of the foundation of probability theory. Problems of Information Transmission, 10(3):206–210, 1974. [55] L. A. Levin. Randomness conservation inequalities: Information and independence in mathematical theories.

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