Kolmogorov complexity

In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of the shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as descriptive complexity, Kolmogorov–Chaitin complexity, algorithmic complexity, algorithmic entropy, or program-size complexity. It is named after Andrey Kolmogorov, who first published on the subject in 1963. The notion of Kolmogorov complexity can be used to state and prove impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, for almost all objects, it is not possible to compute even a lower bound for its Kolmogorov complexity (Chaitin 1964), let alone its exact value.


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