Garden of eden configurations for 2-D cellular automata with rule 2460 N

Siap I., AKIN H., SAH F.

INFORMATION SCIENCES, cilt.180, sa.18, ss.3562-3571, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 180 Sayı: 18
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1016/j.ins.2010.05.039
  • Dergi Adı: INFORMATION SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3562-3571
  • Yıldız Teknik Üniversitesi Adresli: Hayır

Özet

An important problem in cellular automata theory is the reversibility of a cellular automaton which is related to the existence of Garden of Eden configurations in cellular automata. In this paper, we study new local rules for two-dimensional cellular automata over the ternary field Z(3) (the set of integers modulo three) with some of their important characteristics. We obtain necessary and sufficient conditions for the existence of Garden of Eden configurations for two-dimensional ternary cellular automata. Also by making use of the matrix representation of two-dimensional cellular automata, we provide an algorithm to obtain the number of Garden of Eden configurations for two-dimensional cellular automata defined by rule 2460 N. We present an application of the reversible two-dimensional ternary cellular automata to cryptography. (C) 2010 Elsevier Inc. All rights reserved.