A reliable Turing machine

TL;DR

This paper demonstrates that a universal 1-tape Turing machine can perform arbitrarily large computations reliably despite random noise in its operations, using encoding and techniques from cellular automata.

Contribution

It introduces a method for constructing a noise-tolerant universal Turing machine capable of large computations with low noise probability.

Findings

The machine maintains correctness under small noise probabilities.

Encoding schemes enable reliable computation despite noise.

Techniques from cellular automata are adapted for Turing machines.

Abstract

We consider computations of a Turing machine subjected to noise. In every step, the action (the new state and the new content of the observed cell, the direction of the head movement) can differ from that prescribed by the transition function with a small probability (independently of previous such events). We construct a universal 1-tape Turing machine that for a low enough (constant) noise probability performs arbitrarily large computations. For this unavoidably, the input needs to be encoded -- by a simple code depending on its size. The work uses a technique familiar from reliable cellular automata, complemented by some new ones.