Intuitively, an algorithmically random sequence (or random sequence) is a sequence of binary digits that appears random to any algorithm running on a ...
Oct 12, 2007 · Algorithmic randomness is the study of random individual elements in sample spaces, mostly the set of all infinite binary sequences. An ...
Intuitively, an algorithmically random sequence is a sequence of binary digits that appears random to any algorithm running on a universal Turing machine. The notion can be applied analogously to sequences on any finite alphabet. Random sequences... Wikipedia
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Schnorr proves that a sequence is ML-random iff no constructive martingale succeeds on it. A computable martingale is one where \(d\) itself is computable. He ...
One goal of the theory of algorithmic randomness is to give meaning to the notion of a random individual (infinite) sequence. Questions immediately arise: How ...
: Kolmogorov complexity and algorithmic randomness / A. Shen, V. A. Uspensky, N. Vere shchagin. Other titles: Kolmogorovskaya slozhnost i algoritmieskaya ...
Algorithmic Randomness is a research area of mathematics ded- icated to determining if something is random or not. There are sev- eral definitions and ...
Thus, we would like to say that a sequence is random if every infinite sub- sequence, that is a sequence obtained by removing all but infinitely many digits, ...
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This long-awaited book is an irreplaceable source of well-presented classic and new results in algorithmic randomness and algorithmic complexity. It should be ...
Mar 29, 2024 · In this paper, we use methods from effective probability theory to characterise the probability one set along which convergence to the truth ...
Contents · 1 - Key developments in algorithmic randomness · 2 - Algorithmic randomness in ergodic theory · 3 - Algorithmic randomness and constructive/ ...