The Incompressibility Method

Jiang, Tao; Li, Ming; Vitányi, Paul M. B.

doi:10.1007/3-540-44411-4_3

Cited by 2 publications

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“…El largo de la descripción de x depende de la máquina de Turing, pero solo en una constante aditiva. Si K de una secuencia x de largo n es cercana a n, se dice que x es una secuencia aleatoria de grado n, y por ende no se puede comprimir (Jiang et al 2000, Garey & Johnson 1990).…”

Section: Complejidad De Kolmogorovunclassified

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2013

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Section: Complejidad De Kolmogorovunclassified

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2013

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“…Encoding arguments, now commonly framed under the so-called incompressibility method, sprouted from the study of information complexity as introduced by Kolmogorov, Solomonoff, and Chaitin. This technique has been fruitful in recent history, perhaps most famously being used to give the first nontrivial lower bound for the average running time of Shellsort, and for providing a constructive version of the Lovász local lemma [5,6,20,28,39].…”

Section: Introductionmentioning

confidence: 99%

Encoding Arguments

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We study encoding arguments using partial prefix-free codes, which allow us to prove probabilistic statements using the basic fact that uniformly chosen elements from a set of size n cannot be encoded with fewer than log 2 n bits on average. This technique, in the end, is a more direct version of the incompressibility method from the study of Kolmogorov complexity. We use our technique to produce short original proofs for several results. We also explore extensions of the technique to non-uniform input distributions. Finally, we offer a new manner of encoding which allows for real-valued codeword lengths, thereby refining every other result obtained through encoding.

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The Incompressibility Method

Cited by 2 publications

References 26 publications

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Encoding Arguments

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