Temporally Non-Uniform Cellular Automata: Surjectivity, Reversibility and Cyclic Behavior

TL;DR

This paper investigates the properties of temporally non-uniform cellular automata, focusing on surjectivity, reversibility, and cyclic behavior, providing insights into their dynamic capabilities on finite and infinite lattices.

Contribution

It introduces and analyzes the surjectivity, injectivity, reversibility, and cyclic behavior of one-dimensional t-NUCAs with finite and infinite lattices, expanding understanding of their dynamics.

Findings

Characterized surjectivity and injectivity conditions for t-NUCAs.

Established criteria for reversibility of t-NUCAs.

Analyzed cyclic behavior patterns in finite t-NUCAs.

Abstract

This work studies Temporally Non-Uniform Cellular Automata (t-NUCAs), a variant of non-uniform cellular automata, which temporally use two rules in a sequence during their evolution. The one-dimensional t-NUCAs, under finite as well as infinite lattices, are considered in this work. Surjectivity and injectivity of the t-NUCAs are studied. The reversibility of the t-NUCAs is also explored here. Finally, a study on the cyclic behavior of finite t-NUCAs is presented.