Kolmogorov complexity | Wikipedia audio article

This is an audio version of the Wikipedia Article:


00:01:10 1 Definition
00:05:02 2 Invariance theorem
00:05:12 2.1 Informal treatment
00:06:50 2.2 A more formal treatment
00:07:10 3 History and context
00:08:50 4 Basic results
00:12:22 4.1 Uncomputability of Kolmogorov complexity
00:13:00 4.1.1 A naive attempt at a program to compute iK/i
00:16:12 4.2 Chain rule for Kolmogorov complexity
00:17:38 5 Compression
00:18:22 6 Chaitin's incompleteness theorem
00:20:58 7 Minimum message length
00:25:20 8 Kolmogorov randomness
00:26:30 9 Relation to entropy
00:28:29 10 Applications
00:28:50 11 Conditional versions
00:29:21 12 See also
00:29:31 13 Notes
00:29:46 14 References
00:30:41 15 Further reading



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SUMMARY
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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.