Kolmogorov Derandomization
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.
Domaines
Informatique [cs]Origine | Fichiers produits par l'(les) auteur(s) |
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