Year: 2021
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Çapuni, Ilir, Gács, Peter
Institutions: University of Montenegro, Boston University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4320086241