## An introduction to Kolmogorov complexity and its applications |

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### Other editions - View all

An Introduction to Kolmogorov Complexity and Its Applications Ming Li,Paul Vitányi Limited preview - 2009 |

An Introduction to Kolmogorov Complexity and Its Applications Ming Li,Paul Vitanyi Limited preview - 2013 |

An Introduction to Kolmogorov Complexity and Its Applications Ming Li,Paul Vitanyi Limited preview - 1997 |

### Common terms and phrases

A.N. Kolmogorov additive constant algorithmic entropy Algorithmic Information Theory Assume binary string bits C.H. Bennett Comments compressed computation Consider construct contains defined Definition denote effective enumeration elements encoding enumerable semimeasure Equation Example Exercise exists fixed follows formula G.J. Chaitin Gacs given halting Hence Ibid incompressibility inequality infinite binary sequence initial segment integer Invariance Theorem Km(x Kolmogorov complexity L.A. Levin language Lemma log log logarithmic logn lower bound Martin-L6f Math mathematical monotone natural numbers nodes notion object optimal oracle output P-test pac-learnable partial recursive function polynomial prefix complexity prefix machine prefix-code probabilistic probability distribution probability theory problem proof prove PSPACE random sequences real number recursively enumerable set reversible reversible computation sample space satisfies Section self-delimiting sequential test shortest program Show simulate Solovay step strings of length subset symbol Theorem 2.1 tion total recursive uniform measure universal Turing machine upper bound zero