Small weakly universal Turing machines

TL;DR

This paper presents the smallest known weakly universal Turing machines with specific state-symbol configurations, capable of simulating Rule 110, thus advancing the understanding of minimal computational universality.

Contribution

It introduces new small weakly universal Turing machines with minimal state-symbol pairs, demonstrating universality with fewer resources than previously known.

Findings

Machines with (6, 2), (3, 3), and (2, 4) state-symbol pairs are weakly universal.

These machines successfully simulate Rule 110.

They are the smallest known weakly universal Turing machines.

Abstract

We give small universal Turing machines with state-symbol pairs of (6, 2), (3, 3) and (2, 4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest known weakly universal Turing machines.