K complexity

  • What is K complexity?

    The Kolmogorov complexity K of a finite string x is the information in x defined by the length of the shortest program for a reference Universal Turing Machine (UTM) (encoded in binary bits) that outputs the string x ..

  • What is the complexity of a string?

    More formally, the complexity of a string is the length of the shortest possible description of the string in some fixed universal description language (the sensitivity of complexity relative to the choice of description language is discussed below)..

  • 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 a shortest computer program (in a predetermined programming language) that produces the object as output.
  • More formally, the complexity of a string is the length of the shortest possible description of the string in some fixed universal description language (the sensitivity of complexity relative to the choice of description language is discussed below).
  • The classical coding theorem in Kolmogorov complexity states that if an n-bit string x is sampled with probability δ by an algorithm with prefix-free domain then K(x) ≤ log(1/δ) + O(1).
In algorithmic information theory the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program that  DefinitionInvariance theoremBasic resultsChaitin's incompleteness
More formally, the complexity of a string is the length of the shortest possible description of the string in some fixed universal description language (the  DefinitionInvariance theoremBasic resultsChaitin's incompleteness
The Kolmogorov complexity K of a finite string x is the information in x defined by the length of the shortest program for a reference Universal Turing Machine (UTM) (encoded in binary bits) that outputs the string x .
The Kolmogorov complexity K will be defined as a function from finite binary strings of arbitrary length to the natural numbers N. Thus, K: {0,1}* → N is a function defined on 'objects' represented by binary strings.

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