摘要
Along the same line of research as in [1], in this paper, we consider the followingthree major problems. The first is to study, from the viewpoint of program-size complexity,the properties possessed by Martin-lof (M. L.) infinite random sequences. It is found thatM. L. infinite random sequences are normal and satisfy the law of iterated logarithm. Thesecond is to consider the effective generation of M. L. infinite random sequences. It isfound that by using a standard method (e. g., tossing a fair coin) we can choose M. L.infinite random sequences of any computable probability distribution. The last is how todefine the concept of infinite randomness for noncomputable probability distributions. Twotentative definitions are given, and one of them is discussed at length.
<正> Along the same line of research as in [1], in this paper, we consider the followingthree major problems. The first is to study, from the viewpoint of program-size complexity,the properties possessed by Martin-lof (M. L.) infinite random sequences. It is found thatM. L. infinite random sequences are normal and satisfy the law of iterated logarithm. Thesecond is to consider the effective generation of M. L. infinite random sequences. It isfound that by using a standard method (e. g., tossing a fair coin) we can choose M. L.infinite random sequences of any computable probability distribution. The last is how todefine the concept of infinite randomness for noncomputable probability distributions. Twotentative definitions are given, and one of them is discussed at length.
