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Kolmogorov complexity and symmetric relational structures [article]

W.L. Fouché, P.H. Potgieter
2004 arXiv   pre-print
We study partitions of Fraïssé limits of classes of finite relational structures where the partitions are encoded by infinite binary sequences which are random in the sense of Kolmogorov, Chaitin and Solomonoff  ...  See also [15] , [2] , [9] or [8] . ) An infinite binary string ε is said to be Kolmogorov-Chaitin complex (KC-complex) if and only if ∃m∀nH (ε(n)) ≥ n − m .  ...  For s ∈ {0, 1} * let H(s), the Kolmogorov-complexity of s, be the length of a shortest "program" p ∈ {0, 1} * , such that U (p) = s. ( For the history and underlying intuition of these notions, the reader  ... 
arXiv:cs/0402034v1 fatcat:miptqm4o2nf2pkt35sfheix6lu

Page 2264 of Mathematical Reviews Vol. , Issue 94d [page]

1994 Mathematical Reviews  
This book collects a series of five expository papers on the relation be- tween Kolmogorov complexity and structural complexity theory.  ...  In the investigation of the multiplicative structure of the descent algebra of the symmetric group, A. M. Garsia and C. Reutenauer [Adv.  ... 

Page 5977 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
Another section explores the relation between Kolmogorov complexity and  ...  Kolmogorov and G. J. Chaitin.  ... 

An Algorithmic Complexity Interpretation of Lin's Third Law of Information Theory

Joel Ratsaby
2008 Entropy  
Instead of static entropy we assert that the Kolmogorov complexity of a static structure such as a solid is the proper measure of disorder (or chaoticity).  ...  This explains why more complex static structures are less stable.  ...  As Lin [13] suggests, symmetric static structures (crystals) and nonsymmetrical static structures have different amounts of descriptive information.  ... 
doi:10.3390/entropy-e10010006 fatcat:c2zsot7amjhobfoqae5ombhg4e

Biology is a constructive physics [article]

S.V. Kozyrev
2018 arXiv   pre-print
Yuri Manin's approach to Zipf's law (Kolmogorov complexity as energy) is applied to investigation of biological evolution.  ...  Model of constructive statistical mechanics where complexity is a contribution to energy is proposed to model genomics. Scaling laws in genomics are discussed in relation to Zipf's law.  ...  Complexity as energy In the present section we discuss, following Yu.I.Manin [1] , the relation of Kolmogorov complexity and Zipf's law.  ... 
arXiv:1804.10518v4 fatcat:w6ettsewpnct7pzuj4ivutoq74

Comparing Security Notions of Secret Sharing Schemes

Songsong Dai, Donghui Guo
2015 Entropy  
Different to the entropies, Kolmogorov complexity was also defined and used in study the security of individual instances for secret sharing schemes.  ...  This paper is concerned with these security notions for secret sharing schemes defined by the variational measures, including Shannon entropy, guessing probability, min entropy and Kolmogorov complexity  ...  Author Contributions Both authors have contributed to the study and preparation of the article. Both authors have read and approved the final manuscript.  ... 
doi:10.3390/e17031135 fatcat:ii2ydfczx5gjxak4jfi6xi5fs4

Randomness Representation of Turbulence in Canopy Flows Using Kolmogorov Complexity Measures

Dragutin Mihailović, Gordan Mimić, Paola Gualtieri, Ilija Arsenić, Carlo Gualtieri
2017 Entropy  
Based on the Kolmogorov complexity (KC) [20], Lempel and Ziv developed an algorithm for calculating the measure of randomness (LZA) [21] .  ...  In this paper, a methodology to evaluate the randomness of the turbulence using measures based on the Kolmogorov complexity (KC) is proposed.  ...  An analysis based on the Kolmogorov complexity and measures derived from it (the Kolmogorov complexity spectrum and its highest value) was proposed.  ... 
doi:10.3390/e19100519 fatcat:g2nr4mzl5rgwnivbt7h5m7a4fq

Two-Dimensional Kolmogorov Complexity and Validation of the Coding Theorem Method by Compressibility [article]

Hector Zenil, Fernando Soler-Toscano, Jean-Paul Delahaye, Nicolas Gauvrit
2015 arXiv   pre-print
The technique is interesting because it provides a natural algorithmic process for symmetry breaking generating complex n-dimensional structures from perfectly symmetric and fully deterministic computational  ...  Experiments to validate estimations of algorithmic complexity based on these concepts are presented, showing that the measure is stable in the face of some changes in computational formalism and that results  ...  Figure 5 : Two "climbers" (and all their symmetric cases) found in D(4, 2) 2D . Symmetric objects have higher frequency and therefore lower Kolmogorov complexity.  ... 
arXiv:1212.6745v4 fatcat:wslijre2gzftplxw7iq37s34v4

Symmetric Pseudo-Random Matrices [article]

Ilya Soloveychik, Yu Xiang, Vahid Tarokh
2018 arXiv   pre-print
The Kolmogorov complexity of the proposed matrices equals to that of Golomb sequences and is at most 2log(n) bits.  ...  We consider the problem of generating symmetric pseudo-random sign (+/-1) matrices based on the similarity of their spectra to Wigner's semicircular law.  ...  This means that the intrinsic structure of the Golomb sequences is somehow related to the circulant structure.  ... 
arXiv:1702.04086v8 fatcat:c4fwkx7x7rco7bftcssckkzpne

Limit Cycles Bifurcations for a Class of Kolmogorov Model in Symmetrical Vector Field

Chaoxiong Du, Yirong Liu, Wentao Huang
2014 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering  
The problem of limit cycles for Kolmogorov model is interesting and significant both in theory and applications.  ...  In terms of symmetrical Kolmogorov model, published references are less. In terms of the Hilbert Number of Kolmogorov model, our results are new.  ...  the Research Fund of Hunan Provincial Education Department (11B113) and Hunan Provincial Science and Technology Project (2012FJ3106).  ... 
doi:10.1142/s0218127414500400 fatcat:7ionvf4rxzeebcahkydinkn3vu

Network-to-Network Regularization: Enforcing Occam's Razor to Improve Generalization

Rohan Ghosh, Mehul Motani
2021 Neural Information Processing Systems  
Specifically, empirical studies have shown that among functions which have a good training data fit, functions with lower Kolmogorov complexity (KC) are likely to generalize better, while the opposite  ...  Motivated by these findings, we propose, in this work, a novel measure of complexity called Kolmogorov Growth (KG), which we use to derive new generalization error bounds that only depend on the final  ...  Acknowledgements This research was supported by the National University of Singapore and by A*STAR, CISCO Systems (USA) Pte.  ... 
dblp:conf/nips/GhoshM21 fatcat:hp7v74qc7zha7otbqdwx54fnjy

Two-dimensional Kolmogorov complexity and an empirical validation of the Coding theorem method by compressibility

Hector Zenil, Fernando Soler-Toscano, Jean-Paul Delahaye, Nicolas Gauvrit
2015 PeerJ Computer Science  
The technique is interesting because it provides a natural algorithmic process for symmetry breaking generating complexn-dimensional structures from perfectly symmetric and fully deterministic computational  ...  Experiments to validate estimations of algorithmic complexity based on these concepts are presented, showing that the measure is stable in the face of some changes in computational formalism and that results  ...  In this section we study the relation between K m and approaches to Kolmogorov complexity based on compression.  ... 
doi:10.7717/peerj-cs.23 fatcat:dcsapkfadnhshney46df5wpzmi

Information Processing by Symmetric Inductive Turing Machines

Mark Burgin
2020 Proceedings (MDPI)  
In this paper, we study information processing by symmetric models, which are called symmetric inductive Turing machines and reflexive inductive Turing machines.  ...  To reflect this peculiarity of physical computers, symmetric models of computations and automata were introduced.  ...  An interesting problem for future research is elaboration of algorithmic (Kolmogorov) complexity based on symmetric Turing machines and symmetric inductive Turing machines.  ... 
doi:10.3390/proceedings47010028 fatcat:jazqqll3svdv3ejp5ctwd527cu

Selecting protein fuzzy contact maps through information and structure measures

Carlos Bousoño-Calzón, Alicia Oropesa-García, Natalio Krasnogor
2005 European Society for Fuzzy Logic and Technology  
We discuss this in the paper and show its impact on FGCM.  ...  We have introduced different measures of information which address entropy and structure in the data, and discuss their consistency.  ...  The Kolmogorov complexity of an object gives the length of the shortest program that can generate it and is a quantity closely related to the degree of compression which can be achieved for a sequence  ... 
dblp:conf/eusflat/Bousono-CalzonOK05 fatcat:a7k7jwr4x5cvhkirbjafeprzrm

Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution [article]

Iain Johnston, Kamaludin Dingle, Sam F Greenbury, Chico Q. Camargo, Jonathan P K Doye, Sebastian E Ahnert, ard louis
2021 bioRxiv   pre-print
simpler (and more symmetric) phenotypes.  ...  It suggests that symmetric structures preferentially arise not just due to natural selection, but also because they require less specific information to encode, and are therefore much more likely to appear  ...  Schaper and H. Zenil for discussions.  ... 
doi:10.1101/2021.07.28.454038 fatcat:jbf5zmc52zgk3apuz2pvqhkaaa
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