Complexity and Kolmogorov complexity

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Difference between Complexity and Kolmogorov complexity

Complexity vs. Kolmogorov complexity

Complexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, meaning there is no reasonable higher instruction to define the various possible interactions. 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.

Algorithmic information theory

Algorithmic information theory is a subfield of information theory and computer science that concerns itself with the relationship between computation and information.

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Andrey Kolmogorov

Andrey Nikolaevich Kolmogorov (a, 25 April 1903 – 20 October 1987) was a 20th-century Soviet mathematician who made significant contributions to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.

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Blum axioms

In computational complexity theory the Blum axioms or Blum complexity axioms are axioms that specify desirable properties of complexity measures on the set of computable functions.

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Computer program

A computer program is a collection of instructions for performing a specific task that is designed to solve a specific class of problems.

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Entropy (information theory)

Information entropy is the average rate at which information is produced by a stochastic source of data.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Probability

Probability is the measure of the likelihood that an event will occur.

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Randomness

Randomness is the lack of pattern or predictability in events.

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String (computer science)

In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable.

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Turing completeness

In computability theory, a system of data-manipulation rules (such as a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing complete or computationally universal if it can be used to simulate any Turing machine.

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Turing machine

A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules.

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