On the time complexity of 2-tag systems and small universal Turing machines

TL;DR

This paper demonstrates that 2-tag systems can efficiently simulate Turing machines, leading to polynomial-time simulation by small universal Turing machines, significantly improving previous results and reducing simulation overhead.

Contribution

It establishes a polynomial-time simulation of Turing machines by small universal Turing machines using 2-tag systems, improving over four decades of prior work.

Findings

2-tag systems simulate Turing machines efficiently

Small universal Turing machines now simulate in polynomial time

Significant exponential improvement in simulation overhead

Abstract

We show that 2-tag systems efficiently simulate Turing machines. As a corollary we find that the small universal Turing machines of Rogozhin, Minsky and others simulate Turing machines in polynomial time. This is an exponential improvement on the previously known simulation time overhead and improves a forty year old result in the area of small universal Turing machines.