Computational Aspects of Asynchronous CA

TL;DR

This paper explores the computational capabilities of fully asynchronous cellular automata, focusing on their ability to simulate Turing machines and the associated computational costs, providing a theoretical framework for understanding their universality.

Contribution

It characterizes universal updating sequences for asynchronous cellular automata and analyzes the computational cost of their simulation of Turing machines.

Findings

Identifies which updating sequences enable ACA to simulate any Turing machine.

Provides bounds on the computational cost of ACA simulations.

Establishes a theoretical foundation for the universality of asynchronous cellular automata.

Abstract

This work studies some aspects of the computational power of fully asynchronous cellular automata (ACA). We deal with some notions of simulation between ACA and Turing Machines. In particular, we characterize the updating sequences specifying which are "universal", i.e., allowing a (specific family of) ACA to simulate any TM on any input. We also consider the computational cost of such simulations.