# The Power of One-State Turing Machines

## TL;DR

This paper explores the computational power of one-state Turing machines, demonstrating they can recognize complex languages beyond regular and context-free, surpassing pushdown automata in certain tasks.

## Contribution

It extends previous results by proving one-state Turing machines can recognize non context-free languages, showing greater computational power than previously known.

## Key findings

- One-state Turing machines can accept non regular languages.
- They can recognize some non context-free languages.
- They are more powerful than pushdown automata for certain tasks.

## Abstract

At first glance, one-state Turing machines are very weak: the halting problem for them is decidable, and, without memory, they cannot even accept a simple one element language such as $L = \{ 1 \}$ . Nevertheless it has been showed that a one-state Turing machine can accept non regular languages. We extend such result and prove that they can also recognize non context-free languages, so for some tasks they are more powerful than pushdown automata.