70 citations · 229 across the 50 of their papers we have counts for
54 papers
Ergodic theorem and algorithmic randomness
Alexander Shen
We prove the constructive version of Birkhoff's ergodic theorem following Vyugin but trying to separate and state explicitly the combinatorial statement on which this proof is base…
Constructive mathematics and teaching
Alexander Shen
Constructivists (and intuitionists in general) asked what kind of mental construction is needed to convince ourselves (and others) that some mathematical statement is true. This qu…
Kolmogorov Last Discovery? (Kolmogorov and Algorithmic Statictics)
Alexey Semenov, Alexander Shen, Nikolay Vereshchagin
The last theme of Kolmogorov's mathematics research was algorithmic theory of information, now often called Kolmogorov complexity theory. There are only two main publications of Ko…
Inequalities for entropies and dimensions
Alexander Shen
We show that linear inequalities for entropies have a natural geometric interpretation in terms of Hausdorff and packing dimensions, using the point-to-set principle and known resu…
27 Open Problems in Kolmogorov Complexity
Andrei Romashchenko, Alexander Shen, Marius Zimand
The paper proposes open problems in classical Kolmogorov complexity. Each problem is presented with background information and thus the article also surveys some recent studies in…
Individual codewords
Alexander Shen
Algorithmic information theory translates statements about classes of objects into statements about individual objects; it defines individual random sequences, effective Hausdorff…