Invertible behavior in elementary cellular automata with memory

  • Authors:

  • Juan C. Seck-Tuoh-Mora;Genaro J. Martínez;Ramon Alonso-Sanz;Norberto Hernández-Romero

  • Affiliations:

  • Centro de Investigacion Avanzada en Ingenieria Industrial, Universidad Autonoma del Estado de Hidalgo, Hidalgo, Mexico;Instituto de Ciencias Nucleares, Centro de Ciencias de la Complejidad, Universidad Nacional Autonoma de Mexico, Mexico and Unconventional Computing Center, University of the West of England, Unite ...;ETSI Agrónomos, Polytechnic University of Madrid, Madrid, Spain;Centro de Investigacion Avanzada en Ingenieria Industrial, Universidad Autonoma del Estado de Hidalgo, Hidalgo, Mexico

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2012

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Abstract

Elementary cellular automata (ECAs) have been studied for their ability to generate complex global behavior, despite their simplicity. One variation of ECAs is obtained by adding memory to each cell in a neighborhood. This process generates a provisional configuration in which the application of an evolution rule establishes the dynamics of the system. This version is known as an ECA with memory (ECAM). Most previous work on ECAMs analyzed the complex behavior taking chaotic ECAs. However, the present paper investigates reversible ECAMs as obtained from reversible and permutative ECAs. These ECAs have at least one ancestor for every configuration; thus, the correct permutation of states may specify the memory function to obtain reversible ECAMs. For permutative ECAs, which are often irreversible, we demonstrate that the use of a quiescent state and the correct manipulation of de Bruijn blocks produce reversible ECAMs.