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Recursively Enumerable Reals and Chaitin Ω Numbers
"... A real is called recursively enumerable if it is the limit of a recursive, increasing, converging sequence of rationals. Following Solovay [23] and Chaitin [10] we say that an r.e. real dominates an r.e. real if from a good approximation of from below one can compute a good approximation of from b ..."
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Cited by 35 (3 self)
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A real is called recursively enumerable if it is the limit of a recursive, increasing, converging sequence of rationals. Following Solovay [23] and Chaitin [10] we say that an r.e. real dominates an r.e. real if from a good approximation of from below one can compute a good approximation of from below. We shall study this relation and characterize it in terms of relations between r.e. sets. Solovay's [23]like numbers are the maximal r.e. real numbers with respect to this order. They are random r.e. real numbers. The halting probability ofa universal selfdelimiting Turing machine (Chaitin's Ω number, [9]) is also a random r.e. real. Solovay showed that any Chaitin Ω number islike. In this paper we show that the converse implication is true as well: any Ωlike real in the unit interval is the halting probability of a universal selfdelimiting Turing machine.
A Glimpse into Algorithmic Information Theory
 LOGIC, LANGUAGE AND COMPUTATION, VOLUME 3, CSLI SERIES
, 1999
"... This paper is a subjective, short overview of algorithmic information theory. We critically discuss various equivalent algorithmical models of randomness motivating a "randomness hypothesis". Finally some recent results on computably enumerable random reals are reviewed. ..."
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Cited by 6 (6 self)
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This paper is a subjective, short overview of algorithmic information theory. We critically discuss various equivalent algorithmical models of randomness motivating a "randomness hypothesis". Finally some recent results on computably enumerable random reals are reviewed.
A Goodness Measure for Phrase Learning via Compression with the MDL Principle
, 1998
"... This paper reports our ongoing research on unsupervised language learning via compression within the MDL paradigm. It formulates an empirical informationtheoretical measure, description length gain, for evaluating the goodness of guessing a sequence of words (or character) as a phrase (or a word), ..."
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Cited by 4 (2 self)
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This paper reports our ongoing research on unsupervised language learning via compression within the MDL paradigm. It formulates an empirical informationtheoretical measure, description length gain, for evaluating the goodness of guessing a sequence of words (or character) as a phrase (or a word), which can be calculated easily following classic information theory. The paper also presents a bestfirst learning algorithm based on this measure. Experiments on phrase and lexical learning from POS tag and character sequence, respectively, show promising results.
What Is a Random String?
, 1995
"... Chaitin's algorithmic definition of random strings  based on the complexity induced by selfdelimiting computers  is critically discussed. One shows that Chaitin's model satisfy many natural requirements related to randomness, so it can be considered as an adequate model for nite rando ..."
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Cited by 1 (0 self)
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Chaitin's algorithmic definition of random strings  based on the complexity induced by selfdelimiting computers  is critically discussed. One shows that Chaitin's model satisfy many natural requirements related to randomness, so it can be considered as an adequate model for nite random objects. It is a better model than the original (Kolmogorov) proposal. Finally, some open problems will be discussed.
Borel Normality and Algorithmic Randomness
"... We prove that all random sequences (in ChaitinMartinLof sense) and almost all random strings (in both KolmogorovChaitin and Chaitin senses) satisfy various conditions of normality ( rst introduced by Borel). All proofs are constructive. ..."
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We prove that all random sequences (in ChaitinMartinLof sense) and almost all random strings (in both KolmogorovChaitin and Chaitin senses) satisfy various conditions of normality ( rst introduced by Borel). All proofs are constructive.