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An Analysis of Equal Length Cellular Automata (ELCA) Generating Linear Rules for Applications in Distributed Computing
Arnab Mitra, Anirban Kundu, Matangini Chattopadhyay and Samiran Chattopadhyay

Cellular Automata (CA) have been established as a dynamic mathematical modeling tool for scientific and engineering applications. Equal Length Cellular Automata (ELCA) are special classifications of CA having all generated equal length CA subspaces (cycles). Potential usages of ELCA have been reported for engineering applications [1-4]. A detailed analysis of ELCA generating linear and complemented linear rules has been presented in our work. General forms of characteristic matrix and characteristic polynomial for ELCA generation have been reported. Mathematical relationships between cell length of CA and length of generated equal length cycles using explored rules have been reported in the paper.

Keywords: Distributed Computing, Cellular Automata (CA), Equal Length Cellular Automata (ELCA), Characteristics Matrix, Characteristics Polynomial, ELCA Additive Rule.

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