Kolmogorov complexity

Consider flipping a coin 50 times to obtain the binary string 000101000001010100010000010101000100000001010000010. Can we call this random? The string has rather an abundance of 0s, and on closer inspection every other bit is 0. We wouldn’t expect even a biased coin to come up with such a pattern. Still, this string has probability 2-50, just like any other binary string of the same length, so how can we call it any less random?

Kolmogorov ComplexityMathworldPlanetmath provides an answer to these questions in the form of a measure of information content in individual objects. Objects with low information content may be considered non-random. The topic was founded in the 1960s independently by three people: Ray Solomonoff, Andrei Kolmogorov, and Gregory Chaitin.

See Kolmogorov complexity function and invariance theorem for more details.

Title Kolmogorov complexity
Canonical name KolmogorovComplexity
Date of creation 2013-03-22 13:43:41
Last modified on 2013-03-22 13:43:41
Owner tromp (1913)
Last modified by tromp (1913)
Numerical id 9
Author tromp (1913)
Entry type Topic
Classification msc 68Q30
Synonym algorithmic information theory
Synonym algorithmic entropy