# Some Remarks on Real-Time Turing Machines

## TL;DR

This paper explores the computational capabilities of real-time Turing machines with sublinear space, demonstrating they can accept non-regular languages and recognizing exponential time languages via a novel guess and check method.

## Contribution

It corrects a misconception in the literature and introduces a new technique for representing input length in real-time Turing machines.

## Key findings

- Real-time Turing machines can accept non-regular languages.
- A guess and check method enables binary input length representation.
- Unary exponential time languages are recognizable in real-time.

## Abstract

The power of real-time Turing machines using sublinear space is investigated. In contrast to a claim appearing in the literature, such machines can accept non-regular languages, even if working in deterministic mode. While maintaining a standard binary counter appears to be impossible in real-time, we present a guess and check approach that yields a binary representation of the input length. Based on this technique, we show that unary encodings of languages accepted in exponential time can be recognized by nondeterministic real-time Turing machines.