@inproceedings{Li1990KolmogorovCA,
title={Kolmogorov Complexity and its Applications},
author={Ming Li and Paul M. B. Vit{\'a}nyi},
booktitle={Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity},
year={1990}
}

We live in an information society. Information science is our profession. But do you know what is information, mathematically, and how to use it to prove theorems? Examples ! Average case analysis of Shellsort. ! Lovasz Local Lemma ! What is the distance between two pieces of information carrying entities? For example, distance from an internet query to an answer. ! History ! Intuition and ideas in the past ! Inventors ! Basic mathematical theory ! Textbook: Li-Vitanyi: An introduction to… CONTINUE READING

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A characteristic sequence of set A is an infinite binary sequence χ=χ 1 χ 2 …, χ i =1 iff iεA

A characteristic sequence of set A is an infinite…

Proof. (i) Use the number m of 1's in the prefix χ 1:n as termination condition [C(m) ≤ log n+O(1)]

Proof. (i) Use the number m of 1's in the prefix…

Theorem. (i) The characteristic sequence χ of an r.e. set A satisfies C(χ 1:n |n)≤log n+c A for all n. (ii) There is an r.e. set such that C(χ 1:n )≥log n for all n