Translator Disclaimer
December, 2017 Reversibility of Linear Cellular Automata on Cayley Trees with Periodic Boundary Condition
Chih-Hung Chang, Jing-Yi Su
Taiwanese J. Math. 21(6): 1335-1353 (December, 2017). DOI: 10.11650/tjm/8032

Abstract

While one-dimensional cellular automata have been well studied, there are relatively few results about multidimensional cellular automata; the investigation of cellular automata defined on Cayley trees constitutes an intermediate class. This paper studies the reversibility of linear cellular automata defined on Cayley trees with periodic boundary condition, where the local rule is given by $f(x_0,x_1,\ldots,x_d) = b x_0 + c_1 x_1 + \cdots + c_d x_d \pmod{m}$ for some integers $m,d \geq 2$. The reversibility problem relates to solving a polynomial derived from a recurrence relation, and an explicit formula is revealed; as an example, the complete criteria of the reversibility of linear cellular automata defined on Cayley trees over $\mathbb{Z}_2$, $\mathbb{Z}_3$, and some other specific case are addressed. Further, this study achieves a possible approach for determining the reversibility of multidimensional cellular automata, which is known as a undecidable problem.

Citation

Download Citation

Chih-Hung Chang. Jing-Yi Su. "Reversibility of Linear Cellular Automata on Cayley Trees with Periodic Boundary Condition." Taiwanese J. Math. 21 (6) 1335 - 1353, December, 2017. https://doi.org/10.11650/tjm/8032

Information

Received: 29 December 2016; Revised: 11 March 2017; Accepted: 19 March 2017; Published: December, 2017
First available in Project Euclid: 17 August 2017

zbMATH: 06871372
MathSciNet: MR3732909
Digital Object Identifier: 10.11650/tjm/8032

Subjects:
Primary: 37B15

Rights: Copyright © 2017 The Mathematical Society of the Republic of China

JOURNAL ARTICLE
19 PAGES


SHARE
Vol.21 • No. 6 • December, 2017
Back to Top