Christopher P. Porter

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A fruitful way of obtaining meaningful, possibly concrete, algorithmically random numbers is to consider a potential behaviour of a Turing machine and its probability with respect to a measure (or semi-measure) on the input space of binary codes. In this work we obtain characterizations of the algorithmically random reals in higher randomness classes, as(More)
In this article, I consider the status of several statements analogous to the Church-Turing thesis that assert that some definition of algorithmic randomness captures the intuitive conception of randomness. I argue that we should not only reject the theses that have appeared in the algorithmic randomness literature, but more generally that we ought not(More)
Consider a universal Turing machine that produces a partial or total function (or a binary stream), based on the answers to the binary queries that it makes during the computation. We study the probability that the machine will produce a computable function when it is given a random stream of bits as the answers to its queries. Surprisingly, we find that(More)
Kolmogorov complexity measures the algorithmic complexity of a finite binary string σ in terms of the length of the shortest description σ * of σ. Traditionally, the length of a string is taken to measure the amount of information contained in the string. However, we may also view the length of σ as a measure of the cost of producing σ, which permits one to(More)
Although algorithmic randomness with respect to various non-uniform computable measures is well-studied, little attention has been paid to algorithmic randomness with respect to computable trivial measures, where a measure μ on 2 ω is trivial if the support of μ consists of a countable collection of sequences. In this article, it is shown that there is much(More)
In this article, I discuss the extent to which Kolmogorov drew upon von Mises' work in addressing the problem as to why probability is applicable to events in the real world, which I refer to as the applicability problem. In particular, I highlight the role of randomness in Kolmogorov's account, and I argue that this role differs significantly from the role(More)
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