Linear functional classes over cellular automata

TL;DR

This paper explores the capabilities of cellular automata in performing functional computations within low time complexity, analyzing their classes, relationships, and limitations in information transmission.

Contribution

It introduces new functional classes of cellular automata, examines their inclusion relationships, and discusses limits on information transmission beyond recognition tasks.

Findings

Several functional classes of cellular automata are defined and analyzed.

Inclusion relationships among these classes are established.

Limits on information transmission in cellular automata are identified.

Abstract

Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper, we investigate the ability of cellular automata related to functional computation. We introduce several functional classes of low time complexity which contain "natural" problems. We examine their inclusion relationships and emphasize that several questions arising from this functional framework are related to current ones coming from the recognition context. We also provide a negative result which explicits limits on the information transmission whose consequences go beyond the functional point of view.