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 ...
Algorithmically random sequence
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/ ...