REVERSIBLE CELLULAR AUTOMATA WITH PENTA-CYCLIC RULE AND ECCs

Irfan Siap (), Hasan Akin () and Mehmet E. Koroglu ()
Additional contact information
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

International Journal of Modern Physics C (IJMPC), 2012, vol. 23, issue 10, 1-13

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.

Keywords: Cellular automata; periodic boundary condition; reversibility; matrix representations; ECCs; 28D20; 37A35; 37B40; 02.10.Yn; 07.05.Kf; 02.10.De; 05.50.+q (search for similar items in EconPapers)
Date: 2012
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183112500660
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:23:y:2012:i:10:n:s0129183112500660

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183112500660

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().