Kolmogorov Complexity as a Combinatorial Tool

被引:0
作者
Shen, Alexander [1 ]
机构
[1] Univ Montpellier, CNRS, LIRMM, Montpellier, France
来源
TWENTY YEARS OF THEORETICAL AND PRACTICAL SYNERGIES, CIE 2024 | 2024年 / 14773卷
关键词
Kolmogorov complexity; Combinatorial games; Experts aggregation;
D O I
10.1007/978-3-031-64309-5_3
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
Kolmogorov complexity is often used as a convenient language for counting and/or probabilistic existence proofs. However, there are some applications where Kolmogorov complexity is used in a more subtle way. We provide one (somehow) surprising example where an existence of a winning strategy in a natural combinatorial game is proven (and no direct proof is known).
引用
收藏
页码:27 / 31
页数:5
相关论文
共 10 条
[1]   Partitioning multi-dimensional sets in a small number of "uniform" parts [J].
Alon, Noga ;
Newman, Ilan ;
Shen, Alexander ;
Tardos, Gabor ;
Vereshchagin, Nikolai .
EUROPEAN JOURNAL OF COMBINATORICS, 2007, 28 (01) :134-144
[2]   Complex tilings [J].
Durand, Bruno ;
Levin, Leonid A. ;
Shen, Alexander .
JOURNAL OF SYMBOLIC LOGIC, 2008, 73 (02) :593-613
[3]  
Li M, 2008, ICCSE 2008: PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE & EDUCATION, P790
[4]  
Muchnik An. A., 2010, PREPRINT, DOI [10.48550/arXiv.1003.4712, DOI 10.48550/ARXIV.1003.4712]
[5]   An Operational Characterization of Mutual Information in Algorithmic Information Theory [J].
Romashchenko, Andrei ;
Zimand, Marius .
JOURNAL OF THE ACM, 2019, 66 (05)
[6]  
Rosenfeld M, 2023, Arxiv, DOI arXiv:2204.00394
[7]  
Rumyantsev AY, 2006, LECT NOTES COMPUT SC, V3884, P396
[8]  
Shen Alexander, 2011, Computer Science - Theory and Applications. Proceedings of the 6th International Computer Science Symposium in Russia, CSR 2011, P105, DOI 10.1007/978-3-642-20712-9_9
[9]  
Shen A., 2019, Kolmogorov complexity and algorithmic randomness, V220
[10]   Compressibility and Probabilistic Proofs [J].
Shen, Alexander .
UNVEILING DYNAMICS AND COMPLEXITY, CIE 2017, 2017, 10307 :101-111