# Two decades of applied Kolmogorov complexity: in memoriam Andrei Nikolaevich Kolmogorov 1903-87

@article{Li1988TwoDO, title={Two decades of applied Kolmogorov complexity: in memoriam Andrei Nikolaevich Kolmogorov 1903-87}, author={Ming Li and Paul M. B. Vit{\'a}nyi}, journal={[1988] Proceedings. Structure in Complexity Theory Third Annual Conference}, year={1988}, pages={80-101} }

The authors provide an introduction to the main ideas of Kolmogorov complexity and survey the wealth of useful applications of this notion. It is based on a theory of information content of strings, intuitively, that the amount of information in a finite string is the size (i.e. number of bits) of the smallest program that, started with a blank memory, computes the string and then terminates. The following are treated: (1) application of the fact that some strings are compressible; this…

## 59 Citations

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The t-bounded instance complexity of a string x with respect to a set A, ic/sup t/(x:A), is defined as the size of the smallest program that runs in time t, decides x correctly, and makes no mistakes on other strings.

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