Kolmogorov Derandomization - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Kolmogorov Derandomization

Samuel Epstein

Résumé

Using Kolmogorov derandomization, we provide an upper bound on the compression size of numerous solutions. In general, if solutions to a combinatorial problem exist with high probability and the probability is simple, then there exists a simple solution to the problem. Otherwise the problem instance has high mutual information with the halting problem. As a consequence to this, if the probabilistic method can be used to prove the existence of an object, then bounds on its Kolmogorov complexity can be proved as well. This manuscript also introduces game derandomization, where winning probabilistic players imply the existence of winning deterministic players. Multiple applications are included.
Fichier principal
Vignette du fichier
KolmogorovDerandomization.pdf (801.56 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04292439 , version 1 (17-11-2023)
hal-04292439 , version 2 (25-05-2024)

Identifiants

  • HAL Id : hal-04292439 , version 2

Citer

Samuel Epstein. Kolmogorov Derandomization. 2024. ⟨hal-04292439v2⟩
21 Consultations
13 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More