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Page 1914 of Mathematical Reviews Vol. , Issue 97C [page]

1997 Mathematical Reviews  
The main part is on the algorithmic complexity of a string (usually called Kolmogorov complexity).  ...  Upper and lower bounds for these complexities and for their pairwise differences are proven in an informal but clear way.  ... 

Algorithmic Information Theory: a brief non-technical guide to the field [article]

Marcus Hutter
2007 arXiv   pre-print
This is in contrast to classical information theory that is based on random variables and communication, and has no bearing on information and randomness of individual objects.  ...  I would like to thank Paul Vitányi for his help on improving the first draft of this article.  ...  • Algorithmic "Kolmogorov" Complexity (AC) -Philosophical considerations -Properties of AC -Plain (Kolmogorov) complexity -Prefix complexity -Resource bounded complexity -Other complexity variants •  ... 
arXiv:cs/0703024v1 fatcat:7tnvwckblreedgearpvp46vxae

Algorithmic information theory

Marcus Hutter
2007 Scholarpedia  
This is in contrast to classical information theory that is based on random variables and communication, and has no bearing on information and randomness of individual objects.  ...  I would like to thank Paul Vitányi for his help on improving the first draft of this article.  ...  { (p) : U (y, p) = x} • Algorithmic "Kolmogorov" Complexity (AC) -Philosophical considerations -Properties of AC -Plain (Kolmogorov) complexity -Prefix complexity -Resource bounded complexity -Other  ... 
doi:10.4249/scholarpedia.2519 fatcat:i5u2jhvpjnhftnxq26t64aelpi

Is Randomness Native to Computer Science? Ten Years After [chapter]

Marie Ferbus-Zanda, Serge Grigorieff
2011 Randomness Through Computation  
A: There is a version of Omega which works with plain Kolmogorov complexity. Let us first recall what is known with Kolmogorov prefix-free complexity.  ...  With such programming languages, viewed as universal maps, the associated Kolmogorov complexity is the prefix-free one. Q: What about plain Kolmogorov complexity and programming style?  ... 
doi:10.1142/9789814327756_0019 fatcat:lxjyg53fzzb2nlqb6i4oofiicy

On approximate decidability of minimal programs [article]

Jason Teutsch, Marius Zimand
2014 arXiv   pre-print
Our second question, regarding the function which computes minimal indices, is whether one can compute a short list of candidate indices which includes a minimal index for a given program.  ...  Since the 1960's it has been known that, in any reasonable programming language, no effective procedure determines whether or not a given index is minimal.  ...  The authors thank Sanjay Jain for useful comments on the presentation of this work and are grateful to Sasha Shen and Nikolay Vereshchagin for their help with the "warm-up" in Section 2.  ... 
arXiv:1409.0496v1 fatcat:ukz6f6krrjb23gn4ockvrde6ny

Calculating Kolmogorov Complexity from the Output Frequency Distributions of Small Turing Machines [article]

Fernando Soler-Toscano, Hector Zenil, Jean-Paul Delahaye, Nicolas Gauvrit
2014 arXiv   pre-print
Drawing on various notions from theoretical computer science, we present a novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin  ...  complexity of short strings.  ...  The result of a lossless compression algorithm is an upper bound of algorithmic complexity.  ... 
arXiv:1211.1302v2 fatcat:gufuwjoiibaghnyzsefjj6ouwy

Calculating Kolmogorov Complexity from the Output Frequency Distributions of Small Turing Machines

Fernando Soler-Toscano, Hector Zenil, Jean-Paul Delahaye, Nicolas Gauvrit, Matthias Dehmer
2014 PLoS ONE  
Drawing on various notions from theoretical computer science, we present a novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin  ...  complexity of short strings.  ...  The result of a lossless compression algorithm is an upper bound of algorithmic complexity.  ... 
doi:10.1371/journal.pone.0096223 pmid:24809449 pmcid:PMC4014489 fatcat:eqzykdfg2bgl7lmr7l5txnfsmu

Quantum circuit design for universal distribution using a superposition of classical automata [article]

Aritra Sarkar, Zaid Al-Ars, Koen Bertels
2022 arXiv   pre-print
Our implementations on OpenQL and Qiskit quantum programming language is copy-left and is publicly available on GitHub.  ...  In this research, we present a quantum circuit design and implementation for a parallel universal linear bounded automata.  ...  Our proposed computation platform allows approximating these metrics: • Kolmogorov complexity: Kolmogorov complexity (KC), also called algorithmic complexity, is the length of the shortest program that  ... 
arXiv:2006.00987v2 fatcat:ga7lgbhrdnctnecg3oayhi367a

Hierarchical Approximate Proper Orthogonal Decomposition

Christian Himpe, Tobias Leibner, Stephan Rave
2018 SIAM Journal on Scientific Computing  
In both cases, error bounds for prescribed truncation ranks are derived. Another application of the distributed HAPOD is discussed in [8] , which uses the error bound derived in [38] .  ...  No rigorous error bounds are derived, however.  ...  Assuming that the error tolerances \varepsi are chosen according to Theorem 10 for fixed \varepsi \ast , \omega , and assuming that the Kolmogorov widths d N (\scrS ) are bounded for growing \scrS , then  ... 
doi:10.1137/16m1085413 fatcat:3n7n7aqbx5g2bfnjrtnwhxqc4q

Calibrating Randomness

Rod Downey, Denis R. Hirschfeldt, André Nies, Sebastiaan A. Terwijn
2006 Bulletin of Symbolic Logic  
We report on some recent work centered on attempts to understand when one set is more random than another.  ...  For instance, an exciting by-product of the program we describe is a more-or-less natural requirement-free solution to Post's Problem, much along the lines of the Dekker deficiency set.  ...  We thank Joe Miller and the anonymous referee for useful comments on preliminary versions of this paper, and Peter Gács for clarifying certain historical points.  ... 
doi:10.2178/bsl/1154698741 fatcat:msngasauhnhibb7hptoi2unt3a

Mathematical Foundations of Randomness [chapter]

Abhijit Dasgupta
2011 Philosophy of Statistics  
Bandyopadhyay and the anonymous referee for several useful suggestions.  ...  ACKNOWLEDGMENTS The author wishes to thank Ananda Sen for help with some of the references. The author is also indebted to Prasanta S.  ...  Martin-Löf was visiting Kolmogorov in Moscow during 1964-65 and they were working on randomness and complexity of finite objects(Kolmogorov Complexity).  ... 
doi:10.1016/b978-0-444-51862-0.50021-6 fatcat:7pik7bt4hzcureaxtkt4mjcdia

Where Do New Ideas Come From? How Do They Emerge? Epistemology as Computation (Information Processing) [chapter]

Gordana Dodig-Crnkovic
2007 Randomness and Complexity, From Leibniz to Chaitin  
versions of AIT (hands-on programming), are central for the field.  ...  In particular, the main measures of complexity studied in AIT were called Solomonoff-Kolmogorov-Chaitin complexity, Kolmogorov-Chaitin complexity, Kolmogorov complexity, Chaitin complexity, algorithmic  ...  Acknowledgements I am greatly indebted to Paul Vitányi for fostering my research into concrete definitions of Kolmogorov complexity, and to Robert Solovay for illuminating discussions on my definitions  ... 
doi:10.1142/9789812770837_0015 fatcat:hhtjs3z765chpebraxckg3p4hu

Overview of Information Theory, Computer Science Theory, and Stochastic Thermodynamics for Thermodynamics of Computation [article]

David H. Wolpert
2019 arXiv   pre-print
This central expression is crucial for analyzing how the total entropy flow out of a computer depends on its global structure, since that global structure determines the initial distributions into all  ...  I give a quick overview of some of the theoretical background necessary for using modern non-equilibrium statistical physics to investigate the thermodynamics of computation.  ...  Acknowledgements -I would like to thank Josh Grochow and Peter Stadler for helpful discussion, and thank the Santa Fe Institute for helping to support this research. This paper was made  ... 
arXiv:1901.00386v4 fatcat:njjeeo63qnaz5jl2ztyw5ajqru

Equidistribution, Uniform distribution: a probabilist's perspective [article]

Vlada Limic, Nedžad Limić
2018 arXiv   pre-print
The translation from number theory to probability language brings into focus a version of the strong law of large numbers for weakly correlated complex-valued random variables, the study of which was initiated  ...  One purpose of this note is to provide a short introduction for probabilists. We proceed by recalling a perspective originating in a work of the second author from 2002.  ...  Acknowledgments V.L. thanks Chris Burdzy for very useful pointers to the literature, and several constructive comments that reset this research project on the right track, and Martin Goldstern and Pete  ... 
arXiv:1610.02368v2 fatcat:hhsc2onp3ffyzoas6ulvqkfmfu

The Minimum Description Length Principle for Pattern Mining: A Survey [article]

Esther Galbrun
2022 arXiv   pre-print
After giving an outline of relevant concepts from information theory and coding, as well as of work on the theory behind the MDL and similar principles, we review MDL-based methods for mining various types  ...  Finally, we open a discussion on some issues regarding these methods, and highlight currently active related data analysis problems.  ...  Proença and Jilles Vreeken for their comments on the first version of this document.  ... 
arXiv:2007.14009v4 fatcat:jd5ab66jtjevro54docp6qdakm
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