Small Turing universal signal machines

TL;DR

This paper introduces minimal Turing universal signal machines, demonstrating how to construct small, halting universal machines with a limited number of signals and rules from various computational models.

Contribution

It presents the design of the smallest known halting universal signal machine with only 13 meta-signals and 21 collision rules, derived from classical computational models.

Findings

A halting universal signal machine with 13 meta-signals

Construction methods from Turing machines, cellular automata, and cyclic tag systems

Demonstration of minimal signal and rule counts for universality

Abstract

This article aims at providing signal machines as small as possible able to perform any computation (in the classical understanding). After presenting signal machines, it is shown how to get universal ones from Turing machines, cellular-automata and cyclic tag systems. Finally a halting universal signal machine with 13 meta-signals and 21 collision rules is presented.