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RECOGNIZING STRONG RANDOM REALS
RECOGNIZING STRONG RANDOM REALS,10.1017/S1755020308080076,Review of Symbolic Logic,DANIEL OSHERSON,SCOTT WEINSTEIN
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RECOGNIZING STRONG RANDOM REALS
(
Citations: 2
)
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DANIEL OSHERSON
,
SCOTT WEINSTEIN
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 learningtheoretic criterion of 'recognizability'.
Journal:
Review of Symbolic Logic  REV SYMB LOG
, vol. 1, no. 01, 2008
DOI:
10.1017/S1755020308080076
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Citation Context
(2)
...Strong randomness [8,
17
] has various nice characterisations, in particular the following: A is strongly random iff A is MartinL¨ of random and forms a minimal pair with K with respect to Turing reducibility [4, Footnote 2]. For these notions, in order to quantify the degree of nonrandomness of a sequence, one studies from which value f (m) onwards all initial segments can be compressed by m bits...
Rupert Hölzl
,
et al.
Initial Segment Complexities of Randomness Notions
...Furthermore, a set is called “weakly 2random” [20] or “strongly random” [
24
] if and only if it is MartinL¨of random and forms a minimal pair with the halting problem...
Johanna N. Y. Franklin
,
et al.
Relativizations of Randomness and Genericity Notions
References
(20)
Weakly Computable Real Numbers
(
Citations: 35
)
Klaus Ambosspies
,
Klaus Weihrauch
,
Xizhong Zheng
Journal:
Journal of Complexity
, vol. 16, no. 4, pp. 676690, 2000
Calibrating Randomness
(
Citations: 33
)
Rodney G. Downey
,
Denis R. Hirschfeldt
,
André Nies
,
Sebastiaan A. Terwijn
Journal:
The Bulletin of Symbolic Logic  BSL
, vol. 12, no. 3, pp. 411491, 2006
LOWNESS AND 02 NULLSETS
(
Citations: 10
)
ROD DOWNEY
,
ANDRE NIES
,
REBECCA WEBER
,
LIANG YU
Journal:
Journal of Symbolic Logic  JSYML
A Primer on Determinism
(
Citations: 158
)
J. Earman
Published in 1986.
Limiting Recursion
(
Citations: 129
)
E. Mark Gold
Journal:
Journal of Symbolic Logic  JSYML
, vol. 30, no. 1, pp. 2848, 1965
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Citations
(2)
Initial Segment Complexities of Randomness Notions
Rupert Hölzl
,
Thorsten Kräling
,
Frank Stephan
,
Guohua Wu
Conference:
IFIP International Conference on Theoretical Computer Science  IFIP TCS
, pp. 259270, 2010
Relativizations of Randomness and Genericity Notions
(
Citations: 3
)
Johanna N. Y. Franklin
,
Frank Stephan
,
Liang Yu