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REVERSIBLE CELLULAR AUTOMATA WITH PENTA-CYCLIC RULE AND ECCs

Author

Listed:
  • IRFAN SIAP

    (Department of Mathematics, Arts and Science Faculty, Yıldız Technical University, Davutpasa Campus, 34210 Esenler, Istanbul, Turkey)

  • HASAN AKIN

    (Faculty of Education, Zirve University, 27260 Gaziantep, Turkey)

  • MEHMET E. KOROGLU

    (Department of Mathematics, Graduate School, Yildiz Technical University, TR34210 Istanbul, Turkey)

Abstract

The reversibility problem for linear cellular automata with null boundary defined by a rule matrix in the form of a pentadiagonal matrix was studied over the binary field ℤ2by Martín del Reyet al.[Appl. Math. Comput.217, 8360 (2011)]. Recently, the reversibility problem of 1D Cellular automata with periodic boundary has been extended to ternary fields and further to finite primitive fieldsℤpby Cinkiret al.[J. Stat. Phys.143, 807 (2011)]. In this work, we restudy some of the work done in Cinkiret al.[J. Stat. Phys.143, 807 (2011)] by using a different approach which is based on the theory of error correcting codes. While we reestablish some of the theorems already presented in Cinkiret al.[J. Stat. Phys.143, 807 (2011)], we further extend the results to more general cases. Also, a conjecture that is left open in Cinkiret al.[J. Stat. Phys.143, 807 (2011)] is also solved here. We conclude by presenting an application to Error Correcting Codes (ECCs) where reversibility of cellular automata is crucial.

Suggested Citation

  • Irfan Siap & Hasan Akin & Mehmet E. Koroglu, 2012. "REVERSIBLE CELLULAR AUTOMATA WITH PENTA-CYCLIC RULE AND ECCs," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 23(10), pages 1-13.
    • Handle: RePEc:wsi:ijmpcx:v:23:y:2012:i:10:n:s0129183112500660
    DOI: 10.1142/S0129183112500660
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    Cited by:

    1. Hernández Serrano, D. & Martín del Rey, A., 2019. "A closed formula for the inverse of a reversible cellular automaton with (2R+1)-cyclic rule," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 23-34.

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