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Journal articles on the topic 'Randomness complexity'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Downey, Rod. "Computability, Complexity and Randomness." Theory of Computing Systems 52, no. 1 (2012): 1. http://dx.doi.org/10.1007/s00224-012-9430-3.

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2

Karp, Richard M. "Combinatorics, complexity, and randomness." Communications of the ACM 29, no. 2 (1986): 98–109. http://dx.doi.org/10.1145/5657.5658.

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3

Hitchcock, John M., A. Pavan, and N. V. Vinodchandran. "Kolmogorov Complexity in Randomness Extraction." ACM Transactions on Computation Theory 3, no. 1 (2011): 1–12. http://dx.doi.org/10.1145/2003685.2003686.

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4

Chung, Fan R. K., and Prasad Tetali. "Communication Complexity and Quasi Randomness." SIAM Journal on Discrete Mathematics 6, no. 1 (1993): 110–23. http://dx.doi.org/10.1137/0406009.

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5

Kučera, Antonín, and André Nies. "Demuth randomness and computational complexity." Annals of Pure and Applied Logic 162, no. 7 (2011): 504–13. http://dx.doi.org/10.1016/j.apal.2011.01.004.

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6

Blundo, C., A. De Santis, G. Persiano, and U. Vaccaro. "Randomness complexity of private computation." Computational Complexity 8, no. 2 (1999): 145–68. http://dx.doi.org/10.1007/s000370050025.

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7

Zuchowski, Lena C. "Disentangling Complexity from Randomness and Chaos." Entropy 14, no. 2 (2012): 177–212. http://dx.doi.org/10.3390/e14020177.

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8

Wang, Yongge. "Resource bounded randomness and computational complexity." Theoretical Computer Science 237, no. 1-2 (2000): 33–55. http://dx.doi.org/10.1016/s0304-3975(98)00119-4.

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9

Barmpalias, George. "Algorithmic Randomness and Measures of Complexity." Bulletin of Symbolic Logic 19, no. 3 (2013): 318–50. http://dx.doi.org/10.1017/s1079898600010672.

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AbstractWe survey recent advances on the interface between computability theory and algorithmic randomness, with special attention on measures of relative complexity. We focus on (weak) reducibilities that measure (a) the initial segment complexity of reals and (b) the power of reals to compress strings, when they are used as oracles. The results are put into context and several connections are made with various central issues in modern algorithmic randomness and computability.

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10

Wolynes, Peter G. "Randomness and complexity in chemical physics." Accounts of Chemical Research 25, no. 11 (1992): 513–19. http://dx.doi.org/10.1021/ar00023a005.

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11

Shen, A. "Algorithmic Complexity and Randomness: Recent Developments." Theory of Probability & Its Applications 37, no. 1 (1993): 92–97. http://dx.doi.org/10.1137/1137017.

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12

Barmpalias, George. "Algorithmic randomness and measures of complexity." Bulletin of Symbolic Logic 19, no. 3 (2013): 318–50. http://dx.doi.org/10.2178/bsl.1903020.

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13

Goldreich, Oded, and Madhu Sudan. "Special Issue on Randomness and Complexity." SIAM Journal on Computing 36, no. 4 (2006): ix—xi. http://dx.doi.org/10.1137/smjcat0000360000040000ix000001.

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14

CHAITIN, G. J. "RANDOMNESS AND COMPLEXITY IN PURE MATHEMATICS." International Journal of Bifurcation and Chaos 04, no. 01 (1994): 3–15. http://dx.doi.org/10.1142/s0218127494000022.

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One normally thinks that everything that is true is true for a reason. I’ve found mathematical truths that are true for no reason at all. These mathematical truths are beyond the power of mathematical reasoning because they are accidental and random. Using software written in Mathematica that runs on an IBM RS/6000 workstation, I constructed a perverse 200-page algebraic equation with a parameter N and 17,000 unknowns: [Formula: see text] For each whole-number value of the parameter N, we ask whether this equation has a finite or an infinite number of whole number solutions. The answers escape

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15

Chen, Jinhe, Decheng Ding, and Liang Yu. "Conference on Computability, Complexity and Randomness." Bulletin of Symbolic Logic 14, no. 4 (2008): 548–49. http://dx.doi.org/10.2178/bsl/1231081465.

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16

Król, Jerzy, and Paweł Klimasara. "Black Holes and Complexity via Constructible Universe." Universe 6, no. 11 (2020): 198. http://dx.doi.org/10.3390/universe6110198.

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The relation of randomness and classical algorithmic computational complexity is a vast and deep subject by itself. However, already, 1-randomness sequences call for quantum mechanics in their realization. Thus, we propose to approach black hole’s quantum computational complexity by classical computational classes and randomness classes. The model of a general black hole is proposed based on formal tools from Zermelo–Fraenkel set theory like random forcing or minimal countable constructible model Lα. The Bekenstein–Hawking proportionality rule is shown to hold up to a multiplicative constant.

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17

Downey, Rodney G., and Evan J. Griffiths. "Schnorr randomness." Journal of Symbolic Logic 69, no. 2 (2004): 533–54. http://dx.doi.org/10.2178/jsl/1082418542.

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Abstract.Schnorr randomness is a notion of algorithmic randomness for real numbers closely related to Martin-Löf randomness. After its initial development in the 1970s the notion received considerably less attention than Martin-Löf randomness, but recently interest has increased in a range of randomness concepts. In this article, we explore the properties of Schnorr random reals, and in particular the c.e. Schnorr random reals. We show that there are c.e. reals that are Schnorr random but not Martin-Löf random, and provide a new characterization of Schnorr random real numbers in terms of prefi

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18

ICHIMIYA, Masashi. "1010 Randomness Representation in Fluid Flows with Kolmogorov Complexity (Quantification of Randomness)." Proceedings of Conference of Chugoku-Shikoku Branch 2012.50 (2012): 101001–2. http://dx.doi.org/10.1299/jsmecs.2012.50.101001.

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19

Yu, Liang. "Descriptive set theoretical complexity of randomness notions." Fundamenta Mathematicae 215, no. 3 (2011): 219–31. http://dx.doi.org/10.4064/fm215-3-2.

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20

HAMANO, Kenji, and Hirosuke YAMAMOTO. "A Randomness Test Based on T-Complexity." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E93-A, no. 7 (2010): 1346–54. http://dx.doi.org/10.1587/transfun.e93.a.1346.

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21

Rojas, J. Maurice. "Book Review: Kolmogorov complexity and algorithmic randomness." Bulletin of the American Mathematical Society 57, no. 2 (2019): 339–46. http://dx.doi.org/10.1090/bull/1676.

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22

Hitchcock, John M., Jack H. Lutz, and Sebastiaan A. Terwijn. "The arithmetical complexity of dimension and randomness." ACM Transactions on Computational Logic 8, no. 2 (2007): 13. http://dx.doi.org/10.1145/1227839.1227845.

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23

Fouch�, W. L. "Identifying randomness given by high descriptive complexity." Acta Applicandae Mathematicae 34, no. 3 (1994): 313–28. http://dx.doi.org/10.1007/bf00998683.

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24

Goldreich, Oded, and Or Sheffet. "On The Randomness Complexity of Property Testing." computational complexity 19, no. 1 (2010): 99–133. http://dx.doi.org/10.1007/s00037-009-0282-4.

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25

SATOU, Koujirou, and Masashi ICHIMIYA. "1011 Randomness Representation in Fluid Flows with Kolmogorov Complexity(Randomness in Mixing Layer)." Proceedings of Conference of Chugoku-Shikoku Branch 2012.50 (2012): 101101–2. http://dx.doi.org/10.1299/jsmecs.2012.50.101101.

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26

Campani, Carlos A. P., and Paulo Blauth Menezes. "Teorias da Aleatoriedade." Revista de Informática Teórica e Aplicada 11, no. 2 (2004): 75–98. http://dx.doi.org/10.22456/2175-2745.5983.

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This work is a survey about the definition of “random sequence”. We emphasize the definition of Martin-Löf and the definition based on incompressibility (Kolmogorov complexity). Kolmogorov complexity is a profound and sofisticated theory of information and randomness based on Turing machines. These two definitions solve all the problems of the other approaches, satisfying our intuitive concept of randomness, and both are mathematically correct. Furthermore, we show the Schnorr’s approach, that includes a requisite of effectiveness (computability) in his definition. We show the relations betwee

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27

Greenberg, Noam. "Editorial: Special Issue on Computability, Complexity and Randomness." Theory of Computing Systems 58, no. 3 (2015): 381–82. http://dx.doi.org/10.1007/s00224-015-9648-y.

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28

Velupillai, K. Vela. "NON-LINEAR DYNAMICS, COMPLEXITY AND RANDOMNESS: ALGORITHMIC FOUNDATIONS." Journal of Economic Surveys 25, no. 3 (2011): 547–68. http://dx.doi.org/10.1111/j.1467-6419.2010.00668.x.

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29

Miller, Joseph S., and Liang Yu. "On initial segment complexity and degrees of randomness." Transactions of the American Mathematical Society 360, no. 06 (2008): 3193–211. http://dx.doi.org/10.1090/s0002-9947-08-04395-x.

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30

Passy, S. I. "Environmental randomness underlies morphological complexity of colonial diatoms." Functional Ecology 16, no. 5 (2002): 690–95. http://dx.doi.org/10.1046/j.1365-2435.2002.00671.x.

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31

Hölzl, Rupert, and Christopher P. Porter. "Randomness for computable measures and initial segment complexity." Annals of Pure and Applied Logic 168, no. 4 (2017): 860–86. http://dx.doi.org/10.1016/j.apal.2016.10.014.

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32

Canetti, Ran, and Oded Goldreich. "Bounds on tradeoffs between randomness and communication complexity." Computational Complexity 3, no. 2 (1993): 141–67. http://dx.doi.org/10.1007/bf01200118.

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33

Takahashi, Hayato. "Algorithmic randomness and monotone complexity on product space." Information and Computation 209, no. 2 (2011): 183–97. http://dx.doi.org/10.1016/j.ic.2010.10.003.

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34

Downey, Rod, Denis R. Hirschfeldt, André Nies, and Sebastiaan A. Terwijn. "Calibrating Randomness." Bulletin of Symbolic Logic 12, no. 3 (2006): 411–91. http://dx.doi.org/10.2178/bsl/1154698741.

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We report on some recent work centered on attempts to understand when one set is more random than another. We look at various methods of calibration by initial segment complexity, such as those introduced by Solovay [125], Downey, Hirschfeldt, and Nies [39], Downey, Hirschfeldt, and LaForte [36], and Downey [31]; as well as other methods such as lowness notions of Kučera and Terwijn [71], Terwijn and Zambella [133], Nies [101, 100], and Downey, Griffiths, and Reid [34]; higher level randomness notions going back to the work of Kurtz [73], Kautz [61], and Solovay [125]; and other calibrations o

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35

GUAN, SHENG-UEI, and SHU ZHANG. "INCREMENTAL EVOLUTION OF CELLULAR AUTOMATA FOR RANDOM NUMBER GENERATION." International Journal of Modern Physics C 14, no. 07 (2003): 881–96. http://dx.doi.org/10.1142/s0129183103005017.

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Cellular automata (CA) have been used in pseudorandom number generation for over a decade. Recent studies show that controllable CA (CCA) can generate better random sequences than conventional one-dimensional (1D) CA and compete with two-dimensional (2D) CA. Yet the structural complexity of CCA is higher than that of 1D programmable cellular automata (PCA). It would be good if CCA can attain a good randomness quality with the least structural complexity. In this paper, we evolve PCA/CCA to their lowest complexity level using genetic algorithms (GAs). Meanwhile, the randomness quality and outpu

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36

Zamarrud and Muhammed Izharuddin. "8-Bit Quantizer for Chaotic Generator With Reduced Hardware Complexity." International Journal of Rough Sets and Data Analysis 5, no. 3 (2018): 55–70. http://dx.doi.org/10.4018/ijrsda.2018070104.

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This article describes how nowadays, data is widely transmitted over the internet in the real time. Wherever the transmission or storage is required, security is needed. High speed processing hardware machine with reduced complexity are used for the security of the data, that are transmitted in real time. The information which is to be secure are encoded by pseudorandom key. Chaotic numbers are used in place of a pseudorandom key. The generated chaotic values are analogous in nature, these analog values are digitized to generate encryption key like 8-bit, 16-bit, 32-bit. To generate an 8-bit k

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37

Journal, Baghdad Science. "Generating a Strong Key for a Stream Cipher Systems Based on Permutation Networks." Baghdad Science Journal 4, no. 3 (2007): 501–4. http://dx.doi.org/10.21123/bsj.4.3.501-504.

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The choice of binary Pseudonoise (PN) sequences with specific properties, having long period high complexity, randomness, minimum cross and auto- correlation which are essential for some communication systems. In this research a nonlinear PN generator is introduced . It consists of a combination of basic components like Linear Feedback Shift Register (LFSR), ?-element which is a type of RxR crossbar switches. The period and complexity of a sequence which are generated by the proposed generator are computed and the randomness properties of these sequences are measured by well-known randomness t

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38

GU, FANJI, ENHUA SHEN, XIN MENG, YANG CAO, and ZHIJIE CAI. "HIGHER ORDER COMPLEXITY OF TIME SERIES." International Journal of Bifurcation and Chaos 14, no. 08 (2004): 2979–90. http://dx.doi.org/10.1142/s021812740401093x.

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A concept of higher order complexity is proposed in this letter. If a randomness-finding complexity [Rapp & Schmah, 2000] is taken as the complexity measure, the first-order complexity is suggested to be a measure of randomness of the original time series, while the second-order complexity is a measure of its degree of nonstationarity. A different order is associated with each different aspect of complexity. Using logistic mapping repeatedly, some quasi-stationary time series were constructed, the nonstationarity degree of which could be expected theoretically. The estimation of the second

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39

HAMANO, Kenji, Fumio SATO, and Hirosuke YAMAMOTO. "A New Randomness Test Based on Linear Complexity Profile." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E92-A, no. 1 (2009): 166–72. http://dx.doi.org/10.1587/transfun.e92.a.166.

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40

George, Donald A. R. "SHIFTING SANDS: NON-LINEARITY, COMPLEXITY AND RANDOMNESS IN ECONOMICS." Journal of Economic Surveys 25, no. 3 (2011): 634–37. http://dx.doi.org/10.1111/j.1467-6419.2011.00687.x.

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41

Huynh, Dung T. "Nonuniform complexity and the randomness of certain complete languages." Theoretical Computer Science 96, no. 2 (1992): 305–24. http://dx.doi.org/10.1016/0304-3975(92)90340-l.

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42

Martinez-Morales, Manuel, and B. S. Duran. "A test for randomness based on a complexity measure." Communications in Statistics - Theory and Methods 22, no. 3 (1993): 879–95. http://dx.doi.org/10.1080/03610929308831062.

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43

Daugman, John, and Cathryn Downing. "Epigenetic randomness, complexity and singularity of human iris patterns." Proceedings of the Royal Society of London. Series B: Biological Sciences 268, no. 1477 (2001): 1737–40. http://dx.doi.org/10.1098/rspb.2001.1696.

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44

Diaconis, Persi, and Maryanthe Malliaris. "Complexity and randomness in the Heisenberg groups (and beyond)." New Zealand Journal of Mathematics 52 (September 19, 2021): 403–26. http://dx.doi.org/10.53733/134.

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By studying the commuting graphs of conjugacy classes of the sequence of Heisenberg groups $H_{2n+1}(p)$ and their limit $H_\infty(p)$ we find pseudo-random behavior (and the random graph in the limiting case). This makes a nice case study for transfer of information between finite and infinite objects. Some of this behavior transfers to the problem of understanding what makes understanding the character theory of the uni-upper-triangular group (mod p) “wild.” Our investigations in this paper may be seen as a meditation on the question: is randomness simple or is it complicated?

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45

Miller, Joseph S. "Every 2-random real is Kolmogorov random." Journal of Symbolic Logic 69, no. 3 (2004): 907–13. http://dx.doi.org/10.2178/jsl/1096901774.

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Abstract.We study reals with infinitely many incompressible prefixes. Call A ∈ 2ωKolmogorov random if . where C denotes plain Kolmogorov complexity. This property was suggested by Loveland and studied by Martin-Löf. Schnorr and Solovay. We prove that 2-random reals are Kolmogorov random. Together with the converse—proved by Nies. Stephan and Terwijn [11]—this provides a natural characterization of 2-randomness in terms of plain complexity. We finish with a related characterization of 2-randomness.

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46

CAI, ZHIJIE, ENHUA SHEN, FANJI GU, ZHENGJIE XU, JIONG RUAN, and YANG CAO. "A NEW TWO-DIMENSIONAL COMPLEXITY MEASURE." International Journal of Bifurcation and Chaos 16, no. 11 (2006): 3235–47. http://dx.doi.org/10.1142/s0218127406016756.

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In this paper, a new two-dimensional complexity measure, 2D C0 complexity, which is shown to be a reasonable measure under the meaning of randomness finding complexity, is presented and its mathematical properties are proved. This complexity measure is robust for short data and it is calculated easily. An application to characterize the optical imaging orientation functional map in cat visual cortex is also shown.

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47

McCauley, Joseph L. "EQUILIBRIUM VERSUS MARKET EFFICIENCY Randomness versus Complexity in Finance Markets." Journal of Economic Surveys 25, no. 3 (2011): 600–607. http://dx.doi.org/10.1111/j.1467-6419.2011.00685.x.

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48

Bouchaud, Jean-Philippe. "Models of Randomness and Complexity, from Turbulence to Stock Markets." Leonardo 41, no. 3 (2008): 239–43. http://dx.doi.org/10.1162/leon.2008.41.3.239.

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Inspired by the increasing complexity of statistical models for turbulence and stock markets, the author presents some reflections on the very notion of a model and illustrates some relations between physics and aesthetics. He argues that aesthetic emotions arise from a delicate balance between regularity and surprise.

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49

Fischer, Orr, Rotem Oshman, and Uri Zwick. "Public vs. private randomness in simultaneous multi-party communication complexity." Theoretical Computer Science 810 (March 2020): 72–81. http://dx.doi.org/10.1016/j.tcs.2018.04.032.

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50

Li, Hongru, Yaolong Li, Bing Wang, and He Yu. "Randomness complexity as a family feature of rolling bearings’ degradation." Journal of Vibroengineering 21, no. 8 (2019): 2121–39. http://dx.doi.org/10.21595/jve.2019.20528.

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