Transductions Computed by One-Dimensional Cellular Automata

TL;DR

This paper explores the computational power of one-dimensional cellular automata in transforming inputs to outputs, focusing on their ability to perform fast transductions within real-time and linear time constraints, and compares them with other models.

Contribution

It introduces a classification of cellular automaton transductions based on time complexity and demonstrates their superior speed compared to certain sequential models.

Findings

Cellular automaton transducers are as powerful as iterative array transducers in parallel mode.

They outperform iterative arrays in specific time complexity classes.

Cellular automaton transducers can simulate finite state and pushdown transducers faster than iterative arrays.

Abstract

Cellular automata are investigated towards their ability to compute transductions, that is, to transform inputs into outputs. The families of transductions computed are classified with regard to the time allowed to process the input and to compute the output. Since there is a particular interest in fast transductions, we mainly focus on the time complexities real time and linear time. We first investigate the computational capabilities of cellular automaton transducers by comparing them to iterative array transducers, that is, we compare parallel input/output mode to sequential input/output mode of massively parallel machines. By direct simulations, it turns out that the parallel mode is not weaker than the sequential one. Moreover, with regard to certain time complexities cellular automaton transducers are even more powerful than iterative arrays. In the second part of the paper, the model in question is compared with the sequential devices single-valued finite state transducers and deterministic pushdown transducers. It turns out that both models can be simulated by cellular automaton transducers faster than by iterative array transducers.