Skip to main content

An Analytical Formulation for Cellular Automata (CA) Based Solution of Density Classification Task (DCT)

  • Conference paper
Cellular Automata (ACRI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4173))

Included in the following conference series:

Abstract

This paper presents an analytical solution for Density Classification Task (DCT) with an n cell inhomogeneous Cellular Automata represented by its Rule Vector (RV) <R 0 R 1 R 2R i R n − − 1>, where rule R i is employed on i th cell (i=0,1,2,⋯(n-1)). It reports the Best Rule Vector (BRV) for solution of DCT. The concept of Rule Vector Graph (RVG) has provided the framwork for the solution. RVG derived from the RV of a CA can be analyzed to derive the Best Rule Vector (BRV) consisting of only rule 232 and 184 (or 226) for 3-neighborhood CA and their equivalent rules for k-neighborhood CA (k>3). The error analysis of the solution has been also reported.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. von Neumann, J.: The Theory of Self-Reproducing Automata. In: Burks, A.W. (ed.), University of Illinois Press, Urbana and London (1966)

    Google Scholar 

  2. Wolfram, S.: Theory and Application of Cellular Automata. World Scientific, Singapore (1986)

    Google Scholar 

  3. Chaudhuri, P.P., Chowdhury, D.R., Nandi, S., Chatterjee, S.: Additive Cellular Automata, Theory and Applications, vol. 1. IEEE Computer Society Press, Los Alamitos (1997)

    MATH  Google Scholar 

  4. Land, M., Belew, R.K.: No Perfect Cellular Automata For Density Classification Exists. Phyisical Review Letters

    Google Scholar 

  5. Funk, H.: Solution of the Density Classification Problem with Two Cellular Automata Rules. Phys. Rev. E55(3), R2081–R2084 (1997)

    Google Scholar 

  6. Jullie, H., Pollack, J.B.: Coevolving the ’ideal’trainer: Application to the discovary of Cellular Automata Rules. In: Genetic Programming 1998 Proceeding of the Third Annual Conference, Morgan Kaufmann, San Francisco (1998)

    Google Scholar 

  7. Das, M., Crutchfield, J.P.: A Genetic Algorithm Discovers Practicle-based Computation in Cellular Automata. Parallel Problem Solving from Nature III. Springer, Heidelberg

    Google Scholar 

  8. Ferreira, C.: Gene Expression Programming: A New Adaptive Algoithm for Solving Problems. Complex Systems 13(2), 87–129 (2001)

    MATH  MathSciNet  Google Scholar 

  9. Mitchell, M., Crutchfield, P., Hraber, P.T.: Evolving Cellular Automata to Perform Computations: Mechanisms and Impediment. Physica D 75, 361–391 (1994)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Maiti, N.S., Munshi, S., Chaudhuri, P.P. (2006). An Analytical Formulation for Cellular Automata (CA) Based Solution of Density Classification Task (DCT). In: El Yacoubi, S., Chopard, B., Bandini, S. (eds) Cellular Automata. ACRI 2006. Lecture Notes in Computer Science, vol 4173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11861201_20

Download citation

  • DOI: https://doi.org/10.1007/11861201_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40929-8

  • Online ISBN: 978-3-540-40932-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics