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- Alexey Milovanov
- 2016

Algorithmic statistics considers the following problem: given a binary string x (e.g., some experimental data), find a " good " explanation of this data. It uses algorithmic information theory to define formally what is a good explanation. In this paper we extend this framework in two directions. First, the explanations are not only interesting in… (More)

Kolmogorov suggested to measure quality of a statistical hypothesis (a model) P for a data x by two parameters: Kolmogorov complexity C(P) of the hypothesis and the probability P (x) of x with respect to P. The first parameter measures how simple the hypothesis P is and the second one how it fits. The paper [2] discovered a small class of models that are… (More)

Algorithmic statistics is a part of algorithmic information theory (Kolmogorov complexity theory) that studies the following task: given a finite object x (say, a binary string), find an ‘explanation’ for it, i.e., a simple finite set that contains x and where x is a ‘typical element’. Both notions (‘simple’ and ‘typical’) are defined in terms of Kolmogorov… (More)

- Dongmyoung Shin, Sung Gil Park, Byung Soo Song, Eung Su Kim, Oleg Kupervasser, Denis Pivovartchuk +8 others
- ArXiv
- 2013

− In the paper, the problem of precision improvement for the MEMS gyrosensors on indoor robots with horizontal motion is solved by methods of TRIZ ("the theory of inventive problem solving").

Algorithmic statistics considers the following problem: given a binary string x (e.g., some experimental data), find a " good " explanation of this data. It uses algorithmic information theory to define formally what is a good explanation. In this paper we extend this framework in two directions. First, the explanations are not only interesting in… (More)

We improve and simplify the result of the part 4 of " Counting curves and their projections " (Joachim von zur Gathen, Marek Karpinski, Igor Shpar-linski, [1]) by showing that counting roots of a sparse polynomial over F 2 n is #P-and ⊕P-complete under deterministic reductions. 1 Result Consider the field F 2 n. Its elements are presented as polynomials… (More)

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