Compression of enumerations and gain
Computation and Language
2025-06-18 v2 Information Theory
math.IT
Logic
Abstract
We study the compressibility of enumerations in the context of Kolmogorov complexity, focusing on strong and weak forms of compression and their gain: the amount of auxiliary information embedded in the compressed enumeration. The existence of strong compression and weak gainless compression is shown for any computably enumerable (c.e.) set. The density problem of c.e. sets with respect to their prefix complexity is reduced to the question of whether every c.e. set is well-compressible, which we study via enumeration games.
Keywords
Cite
@article{arxiv.2304.03030,
title = {Compression of enumerations and gain},
author = {George Barmpalias and Xiaoyan Zhang and Bohua Zhan},
journal= {arXiv preprint arXiv:2304.03030},
year = {2025}
}