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Using de Bruijn Diagrams to Analyze 1d Cellular Automata Traffic Models

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Cellular Automata (ACRI 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3305))

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Abstract

We used de Bruijn diagrams to analyze traffic models based on one-dimensional cellular automata. The first model is the rule 184 which simulates traffic flow with the simplest dynamics. The second model is a rule represented by a cellular automaton of order (4,2), which includes all the configurations that can be presented when the model contemplates two speeds. To this cellular automata we denominated LCATRAFFICFLOWVMAX2 which is completely deterministic and we can predict or analyze its behavior still before to carry out simulations in computer using de Bruijn diagrams. We obtained this model taking as it bases the model proposed by Nagel-Schreckenberg to simulate traffic flow in one dimension and one direction.

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References

  1. Golomb, S.: Shift Register Sequences. Holden Day, Inc., San Francisco (1967)

    MATH  Google Scholar 

  2. Jen, E.: Scaling of preimages in cellular automata. Complex Systems 1, 1045–1062 (1987)

    MATH  MathSciNet  Google Scholar 

  3. Mcintosh, H.: Linear cellular automata (1990), Webpage: http://delta.cs.cinvestav.mx/~mcintosh

  4. Mcintosh, H.: Linear cellular automata via de Bruijn diagrams (1992), Webpage: http://delta.cs.cinvestav.mx/~mcintosh

  5. Moore, E.: Gedanken Experiments on Sequential MachinesScaling. In: Shannon, C.E., McCarthy, J. (eds.) Automata Studies. Princeton University Press, Princeton (1956)

    Google Scholar 

  6. Mora, J.: Matrix methods and local properties of reversible one-dimensional cellular automata. J. Phys. A: Math. Gen. 35, 5563–5573 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. Nagel, K., Schreckenberg, M.: J. Phys. I (France) 12, 2221 (1992)

    Google Scholar 

  8. Nasu, M.: Local Maps Inducing Surjective Global Maps of One Dimensional Tessellation Automata. Mathematical Systems Theory 11, 327–351 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ralston, A.: De Bruijn Sequences-A Model Example of the Interaction of Discrete Mathematics and Computer Science. Mathematics Magazine 55, 131–143 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  10. Rodriguez, R.: Modelación de flujo de tránsito de autos utilizando autómatas celulares. Graduate thesis (2002), Webpage: http://delta.cs.cinvestav.mx/~mcintosh

  11. Wolfram, S.: Computation theory of cellular automata. Communications in Mathematical Physics 96, 15–57 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  12. Wolfram, S.: Statistical mechanics of cellular automata. Reviews of Modern Physics 55, 601–644 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  13. Wolfram, S.: Theory and Applications of cellular automata. World Scientific, Singapore (1986)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Departamento de Ingeniería Eléctrica, Sección Computación, Centro de Investigación y de Estudios Avanzados del IPN, Av. IPN 2508, San Pedro Zacatenco, D.F., México, 07360

    René Rodríguez Zamora & Sergio Víctor Chapa Vergara

Authors
  1. René Rodríguez Zamora
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  2. Sergio Víctor Chapa Vergara
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Editor information

Editors and Affiliations

  1. Faculty of Sciences, Section of Computational Science, University of Amsterdam, Kruislaan 403, 1098 SJ, Amsterdam, The Netherlands

    Peter M. A. Sloot

  2. Computer Science Department, University of Geneva, Switzerland

    Bastien Chopard

  3. Section Computational Science, University of Amsterdam, The Netherlands

    Alfons G. Hoekstra

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© 2004 Springer-Verlag Berlin Heidelberg

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Zamora, R.R., Vergara, S.V.C. (2004). Using de Bruijn Diagrams to Analyze 1d Cellular Automata Traffic Models. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds) Cellular Automata. ACRI 2004. Lecture Notes in Computer Science, vol 3305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30479-1_32

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  • DOI: https://doi.org/10.1007/978-3-540-30479-1_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23596-5

  • Online ISBN: 978-3-540-30479-1

  • eBook Packages: Springer Book Archive

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