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Page 1914 of Mathematical Reviews Vol. , Issue 97C
[page]
1997
Mathematical Reviews
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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]
2007
arXiv
pre-print
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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
2007
Scholarpedia
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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]
2011
Randomness Through Computation
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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]
2014
arXiv
pre-print
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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]
2014
arXiv
pre-print
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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
2014
PLoS ONE
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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]
2022
arXiv
pre-print
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2020 pre-print arXiv:2006.00987v1 fatcat:xlm7izrgsjfypn32dx3n6f4csq
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
2018
SIAM Journal on Scientific Computing
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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
2006
Bulletin of Symbolic Logic
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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]
2011
Philosophy of Statistics
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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]
2007
Randomness and Complexity, From Leibniz to Chaitin
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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]
2019
arXiv
pre-print
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2019 pre-print arXiv:1901.00386v3 fatcat:y2ulsn5udjhcvdqtxqqkeqthq4Other Versions
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]
2018
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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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