Keyword

algorithmic randomness

Description: A mathematical theory characterizing randomness through computability and information content, with applications in logic, probability, and computer science.

Primary topic: Computability, Logic, AI Algorithms (83%)

OpenAlex ID: keywords/algorithmic-randomness

The definition of random sequences

1966 · Per Martin-Löf · Information and Control · 1,221

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Algorithmic Randomness and Complexity

2010 · Rodney G. Downey, Denis R. Hirschfeldt · Theory and applications of computability · 919

Computability and Randomness

2009 · André Nies · Oxford University Press eBooks · 617

Book Review: An introduction to Kolmogorov Complexity and its Applications Second Edition, 1997 by Ming Li and Paul Vitanyi (Springer (Graduate Text Series))

1997 · William Gasarch · ACM SIGACT News · 583

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Algorithmic Information Theory

1987 · Gregory. J. Chaitin · Cambridge University Press eBooks · 461

Algorithmic randomness and physical entropy

1989 · W. H. Zurek · Physical Review A · 366

A unified approach to the definition of random sequences

1971 · C. P. Schnorr · Theory of Computing Systems · 249

Machine-Learning Applications of Algorithmic Randomness

1999 · Vladimir Vovk, Alex Gammerman, et al. · ePrints Soton (University of Southampton) · 164

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Algorithms and Randomness

1988 · A. N. Kolmogorov, V. A. Uspenskii · Theory of Probability and Its Applications · 160

Uniform test of algorithmic randomness over a general space

2005 · Peter Gács · Theoretical Computer Science · 139

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Kolmogorov Complexity and Algorithmic Randomness

2017 · A. Shen, V. Uspensky, et al. · Mathematical surveys and monographs · 130

Randomness, relativization and Turing degrees

2005 · André Nies, Frank Stephan, et al. · Journal of Symbolic Logic · 130

Feynman and Computation

2018 · Anthony Hey · CRC Press eBooks · 128

Computability of probability measures and Martin-Löf randomness over metric spaces

2009 · Mathieu Hoyrup, Cristóbal Rojas · Information and Computation · 123

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A Decomposition Method for Global Evaluation of Shannon Entropy and Local Estimations of Algorithmic Complexity

2018 · Hector Zenil, Santiago Hernández-Orozco, et al. · Entropy · 116

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Algorithmic randomness and complexity. Theory and Applications of Computability

2012 · Rodney G. Downey, Denis R. Hirschfeldt · 102

Randomness and Computability: Open Questions

2006 · Joseph S. Miller, André Nies · Bulletin of Symbolic Logic · 89

Zufälligkeit und Wahrscheinlichkeit : Eine algorithmische Begründung der Wahrscheinlichkeitstheorie

1970 · C. P. Schnorr · 88

Experimental evidence of quantum randomness incomputability

2010 · Cristian S. Calude, Michael J. Dinneen, et al. · Physical Review A · 84

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Using random sets as oracles

2007 · Denis R. Hirschfeldt, André Nies, et al. · Journal of the London Mathematical Society · 84

Algorithmic properties of structures

1967 · Erwin Engeler · Theory of Computing Systems · 83

Information and randomness: An algorithmic perspective

2003 · Computers & Mathematics with Applications · 82

$$\textit{K}$$-trivial, $$\textit{K}$$-low and $${{\mathrm{\textit{MLR}}}}$$-low Sequences: A Tutorial

2015 · Laurent Bienvenu, Alexander Shen · Lecture notes in computer science · 75

The Fundamental Nature of the Log Loss Function

2015 · Vladimir Vovk · Lecture notes in computer science · 71

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Ergodic theorems for individual random sequences

1998 · V.V. V'yugin · Theoretical Computer Science · 65

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Works count: 1,110

Citation count: 10,510