Recognizing Strong Random Reals

The class of strong random reals can be defined via a natural conception of effective null set. We show that the same class is also characterized by a learning-theoretic criterion of 'recognizability'.

[1]  V. Uspenskii,et al.  Can an individual sequence of zeros and ones be random? Russian Math , 1990 .

[2]  Antony Eagle,et al.  Randomness Is Unpredictability , 2005, The British Journal for the Philosophy of Science.

[3]  A. Kucera Measure, Π10-classes and complete extensions of PA , 1985 .

[4]  J. Moser Stable and Random Motions in Dynamical Systems: With Special Emphasis on Celestial Mechanics. , 1973 .

[5]  R. Mises Grundlagen der Wahrscheinlichkeitsrechnung , 1919 .

[6]  Oded Goldreich Foundations of Cryptography: Index , 2001 .

[7]  Oded Goldreich,et al.  Foundations of Cryptography: Volume 1, Basic Tools , 2001 .

[8]  Rodney G. Downey,et al.  Algorithmic Randomness and Complexity , 2010, Theory and Applications of Computability.

[9]  Erhard Tornier,et al.  Grundlagen der Wahrscheinlichkeitsrechnung , 1933 .

[10]  J. C. Oxtoby Measure and Category , 1971 .

[11]  Claus-Peter Schnorr,et al.  The process complexity and effective random tests. , 1972, STOC.

[12]  André Nies,et al.  Calibrating Randomness , 2006, Bull. Symb. Log..

[13]  D. Saari,et al.  Stable and Random Motions in Dynamical Systems , 1975 .

[14]  Péter Gács,et al.  Every Sequence Is Reducible to a Random One , 1986, Inf. Control..

[15]  Paul M. B. Vitányi,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 1993, Graduate Texts in Computer Science.

[16]  Oded Goldreich,et al.  Foundations of Cryptography: List of Figures , 2001 .

[17]  Hilary Putnam,et al.  Trial and error predicates and the solution to a problem of Mostowski , 1965, Journal of Symbolic Logic.

[18]  D. Wan AN ELEMENTARY PROOF OF A THEOREM OF KATZ , 1989 .

[19]  Rebecca Weber,et al.  Lowness and nullsets , 2006, Journal of Symbolic Logic.

[20]  A. Church On the concept of a random sequence , 1940 .

[21]  Klaus Weihrauch,et al.  Weakly Computable Real Numbers , 2000, J. Complex..

[22]  E. Mark Gold,et al.  Limiting recursion , 1965, Journal of Symbolic Logic.

[23]  Per Martin-Löf,et al.  The Definition of Random Sequences , 1966, Inf. Control..

[24]  John Earman,et al.  A Primer on Determinism , 1986 .

[25]  A. Nies,et al.  Lowness and Π 0 2 Nullsets , 2006 .

[26]  Daniel N. Osherson,et al.  Elementary Proof of a Theorem of Jean Ville , 2006, ArXiv.

[27]  J. C. Oxtoby,et al.  Measure and Category: A Survey of the Analogies between Topological and Measure Spaces , 1971 .