Kolmogorov time hierarchy and novelty games - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

Kolmogorov time hierarchy and novelty games

Hiérarchie temporelle de Kolmogorov et jeux de trouvailles

Résumé

In this paper we improve on the state-of-the-art time hierarchy for time-bounded Kolmogorov complexity. More precisely, we prove that there are infinitely many $n∈ \mathbf{N}$ such that there are strings of size $n$ which are the output of programs of size $f=o(\log n)$ running in $o(2^fT)$ steps but are not the output of any program of size $f$ running in $T$ steps. The previous gap was exponential in $2^f$. This result is established by studying a new problem in combinatorics: a list $E$ of $pk$ numbers in $[1;N]$ is shared evenly between $p$ players, who each get to output an answer depending on their share of $E$. The players must establish a communication-free strategy ensuring that one of them outputs a number not belonging to $E$.
Fichier principal
Vignette du fichier
kolmogorov_time_hierarchy (5).pdf (566.43 Ko) Télécharger le fichier
Licence : CC BY - Paternité

Dates et versions

hal-04539439 , version 1 (09-04-2024)

Licence

Paternité

Identifiants

  • HAL Id : hal-04539439 , version 1

Citer

Ulysse Léchine, Thomas Seiller. Kolmogorov time hierarchy and novelty games. 2024. ⟨hal-04539439⟩
0 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More