On Schnorr and computable randomness, martingales, and machines

We examine the randomness and triviality of reals using notions arising from martingales and prefix-free machines. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

[1]  André Nies,et al.  Trivial Reals , 2002, CCA.

[2]  Ming Li,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 2019, Texts in Computer Science.

[3]  Klaus Ambos-Spies,et al.  Randomness in Computability Theory , 2000 .

[4]  Rodney G. Downey,et al.  Schnorr Randomness , 2002, Electron. Notes Theor. Comput. Sci..

[5]  Paul M. B. Vitányi,et al.  Randomness , 2001, ArXiv.

[6]  André Nies,et al.  Randomness, relativization and Turing degrees , 2005, J. Symb. Log..

[7]  André Nies,et al.  Randomness, Computability, and Density , 2002, SIAM J. Comput..

[8]  Ludwig Staiger,et al.  The Kolmogorov complexity of real numbers , 1999, Theor. Comput. Sci..

[9]  L. Levin,et al.  THE COMPLEXITY OF FINITE OBJECTS AND THE DEVELOPMENT OF THE CONCEPTS OF INFORMATION AND RANDOMNESS BY MEANS OF THE THEORY OF ALGORITHMS , 1970 .

[10]  Antonín Kucera,et al.  Randomness and Recursive Enumerability , 2001, SIAM J. Comput..

[11]  ComplexityValentine KabanetsDecember Randomness and Complexity , 1997 .

[12]  C. Schnorr Zufälligkeit und Wahrscheinlichkeit , 1971 .

[13]  Max L. Warshauer,et al.  Lecture Notes in Mathematics , 2001 .

[14]  André Nies,et al.  Reals which Compute Little , 2002 .

[15]  Rodney G. Downey,et al.  Randomness and reducibility , 2001, J. Comput. Syst. Sci..

[16]  R. Soare Recursively enumerable sets and degrees , 1987 .

[17]  Sebastiaan Terwijn,et al.  Computational randomness and lowness* , 2001, Journal of Symbolic Logic.