On Linear Cellular Automata
wolfram cellular automata are considered and their operation is demonstrated using an example of traffic flow simulation. For the class of one-dimensional elementary cellular automata, the concept of linearity is introduced in the language of Zhegalkin operators. An algorithm for finding linear Zheg...
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| Published in | Programming and computer software Vol. 50; no. 1; pp. 24 - 30 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.02.2024
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0361-7688 1608-3261 |
| DOI | 10.1134/S0361768824010067 |
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| Abstract | wolfram cellular automata are considered and their operation is demonstrated using an example of traffic flow simulation. For the class of one-dimensional elementary cellular automata, the concept of linearity is introduced in the language of Zhegalkin operators. An algorithm for finding linear Zhegalkin operators with multipliers of three variables is presented. The algorithm is implemented in Python. |
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| AbstractList | wolfram cellular automata are considered and their operation is demonstrated using an example of traffic flow simulation. For the class of one-dimensional elementary cellular automata, the concept of linearity is introduced in the language of Zhegalkin operators. An algorithm for finding linear Zhegalkin operators with multipliers of three variables is presented. The algorithm is implemented in Python. |
| Author | Timofeev, I. V. Fedchenko, D. P. Kytmanov, A. A. Poroshin, A. O. Kulikov, V. R. |
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| Cites_doi | 10.1016/j.simpat.2022.102519 10.1016/j.matcom.2009.02.011 10.1109/NANO.2003.1231740 10.3390/rs14041014 10.1103/PhysRevE.106.044705 10.1109/12.888056 10.1007/978-0-387-30440-3_69 10.1103/RevModPhys.55.601 10.1016/0020-0190(93)90061-D 10.3390/math7090816 10.3390/sym14122673 |
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| Copyright | Pleiades Publishing, Ltd. 2024. ISSN 0361-7688, Programming and Computer Software, 2024, Vol. 50, No. 1, pp. 24–30. © Pleiades Publishing, Ltd., 2024. Russian Text © The Author(s), 2024, published in Programmirovanie, 2024, Vol. 50, No. 1. |
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| References_xml | – reference: Gal'perinG.A.ZemlyakovA.N.Mathematical Billiards: Billiard Problems and Related Problems of Mathematics and Mechanics1990MoscowNauka[in Russian] – reference: MartinA.Reversibility of linear cellular automataAppl. Math. Comput.2011217836083662802245 – reference: Sato, T., Decidability for some problems of linear cellular automata over finite commutative rings, Inf. Proc. Lett., 993, vol 46, no. 3, pp. 151–155. – reference: Cagigas-Muniz, D. et al., Efficient simulation execution of cellular automata on GPU, Simul. Modell. Pract. Theory, 2022, vol. 118, p. 102519. – reference: WolframS.Statistical mechanics of cellular automataRev. Modern Phys.19835560170907710.1103/RevModPhys.55.601 – reference: FedchenkoD.P.KimP.N.TimofeevI.V.Photonic topological insulator based on frustrated total internal reflection in array of coupled prism resonatorsSymmetry202214267310.3390/sym14122673 – reference: GasnikovA.Introduction to Mathemetical Modeling of Traffic Flows2022[in Russian] – reference: Lemont, B.K. and Seybold, P.G., Cellular automata modeling of complex biochemical systems, in Encyclopedia of Complexity and Systems Science, 2015. – reference: Martin del ReyA.Casado VaraR.HernándezS. D.Reversibility of symmetric linear cellular automata with radius r = 3Mathematics2019781610.3390/math7090816 – reference: FronczakP.Cellular automata approach to modeling self-organized periodic patterns in nanoparticle-doped liquid crystalsPhys. Rev. E.20221064470510.1103/PhysRevE.106.044705 – reference: Conway, J. et al., The game of life, Sci. Amer., vol. 223, no. 4, p. 4. – reference: JanssensK.G.F.An introductory review of cellular automata modeling of moving grain boundaries in polycrystalline materialsMath. Comput. in Simul.20108013611381264727310.1016/j.matcom.2009.02.011 – reference: KozhoridzeG.DorE.B.SternbergM.Assessing the dynamics of plant species invasion in Eastern-Mediterranean Coastal Dunes Using Cellular Automata Modeling and Satellite Time-Series AnalysesRemote Sens.202214101410.3390/rs14041014 – reference: TomassiniM.SipperM.PerrenoudM.On the generation of high-quality random numbers by two-dimensional cellular automataIEEE Trans. Comput.2000491146115110.1109/12.888056 – reference: Fedchenko, D.P., Novikov, V.V., and Timofeev I.V., Photonic topological insulators of the Rudner type in terms of of tricolor cellular automata, Uch. Zap. Fiz. Fakul’teta MGU, 2021, No. 5, p. 2150302. – reference: Batty, M. 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Env. – volume-title: Introduction to Mathemetical Modeling of Traffic Flows year: 2022 ident: 3819_CR6 – ident: 3819_CR19 – volume: 80 start-page: 1361 year: 2010 ident: 3819_CR8 publication-title: Math. Comput. in Simul. doi: 10.1016/j.matcom.2009.02.011 – volume: 139 start-page: 830 year: 1961 ident: 3819_CR2 publication-title: Dokl. Akad. Nauk SSSR – volume: 5 start-page: 130 year: 2002 ident: 3819_CR12 publication-title: Wolfram Media – volume: 2 start-page: 160 year: 2003 ident: 3819_CR14 publication-title: NanoTechnology Conference doi: 10.1109/NANO.2003.1231740 – volume: 14 start-page: 1014 year: 2022 ident: 3819_CR10 publication-title: Remote Sens. doi: 10.3390/rs14041014 – volume: 106 start-page: 44705 year: 2022 ident: 3819_CR7 publication-title: Phys. Rev. E. doi: 10.1103/PhysRevE.106.044705 – volume: 49 start-page: 1146 year: 2000 ident: 3819_CR13 publication-title: IEEE Trans. Comput. doi: 10.1109/12.888056 – ident: 3819_CR4 doi: 10.1007/978-0-387-30440-3_69 – volume: 55 start-page: 601 year: 1983 ident: 3819_CR11 publication-title: Rev. Modern Phys. doi: 10.1103/RevModPhys.55.601 – ident: 3819_CR16 doi: 10.1016/0020-0190(93)90061-D – volume: 217 start-page: 8360 year: 2011 ident: 3819_CR17 publication-title: Appl. Math. Comput. – volume-title: Mathematical Billiards: Billiard Problems and Related Problems of Mathematics and Mechanics year: 1990 ident: 3819_CR22 – volume-title: Theory of Self-Reproducing Automata year: 1966 ident: 3819_CR1 – volume: 7 start-page: 816 year: 2019 ident: 3819_CR18 publication-title: Mathematics doi: 10.3390/math7090816 – volume: 14 start-page: 2673 year: 2022 ident: 3819_CR21 publication-title: Symmetry doi: 10.3390/sym14122673 – ident: 3819_CR9 – ident: 3819_CR3 |
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| SubjectTerms | Algorithms Artificial Intelligence Boolean Cellular automata Codes Computer Science Flow simulation Linearity Neighborhoods Operating Systems Operators Programming languages Quantum dots Software Engineering Software Engineering/Programming and Operating Systems |
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