• Publications
  • Influence
Randomness and lowness notions via open covers
TLDR
We show that a wide variety of lowness notions can be expressed in a similar way, i.e., via the ability to cover open sets of a certain type by opensets of some other type. Expand
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Reconciling Data Compression and Kolmogorov Complexity
TLDR
Kolmogorov complexity defined via decidable machines yields characterizations in terms of the intial segment complexity of sequences of the concepts of Martin-Lof randomness, Schnorr randomness and Kurtz randomness. Expand
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Kolmogorov Complexity and Solovay Functions
TLDR
We show that there exists a computable upper bound f of the prefix-free Kolmogorov complexity function K such that f (x) = K(x) for infinitely many x. Expand
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On the history of martingales in the study of randomness
Martingales played an important role in the study of randomness in the twentieth century. Jean Ville invented martingales in the 1930s in order to improve Richard von Mises' concept of a collective,Expand
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Algorithmic Identification of Probabilities Is Hard
TLDR
We study in this paper a similar question, but from the viewpoint of inductive inference, and give a negative answer to this question. Expand
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Algorithmic tests and randomness with respect to a class of measures
TLDR
This paper offers some new results on randomness with respect to classes of measures, along with a didactic exposition of their context based on results that appeared elsewhere. Expand
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Ergodic-Type Characterizations of Algorithmic Randomness
TLDR
A theorem of Kucera states that given a Martin-Lof random infinite binary sequence ω and an effectively open set A of measure less than 1, some tail of ω is not in A. Expand
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Effective Randomness for Computable Probability Measures
TLDR
We determine all the implications that hold between the equivalence relations induced by Martin-Lof Randomness, computable randomness, Schnorr randomness and weak randomness. Expand
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Von Neumann's Biased Coin Revisited
  • L. Bienvenu, B. Monin
  • Computer Science
  • 27th Annual IEEE Symposium on Logic in Computer…
  • 25 June 2012
Suppose you want to generate a random sequence of zeros and ones and all you have at your disposal is a coin which you suspect to be biased (but do not know the bias). Can "perfect" randomness beExpand
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A constructive version of Birkhoff's ergodic theorem for Martin-Löf random points
TLDR
We prove the effective version of [email protected]s ergodic theorem for Martin-Lof random points and effectively open sets, improving the results previously obtained in this direction (in particular those of Vyugin and Hoyrup, Rojas). Expand
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