Woods, Damien and Neary, Turlough (2009) Small Semi-Weakly Universal Turing Machines. Fundamenta Informaticae, 91 (1). pp. 179-195. ISSN 0169-2968

Preview

Download (128kB) | Preview

Abstract

We present three small universal Turing machines that have 3 states and 7 symbols, 4 states and 5 symbols, and 2 states and 13 symbols, respectively. These machines are semi-weakly universal which means that on one side of the input they have an infinitely repeated word, and on the other side there is the usual infinitely repeated blank symbol. This work can be regarded as a continuation of early work by Watanabe on semi-weak machines. One of our machines has only 17 transition rules, making it the smallest known semi-weakly universal Turing machine. Interestingly, two of our machines are symmetric with Watanabe's 7-state and 3-symbol, and 5-state and 4-symbol machines, even though we use a different simulation technique.

Item Type:	Article
Additional Information:	Note that the pdf has incorrect page numbers
Keywords:	4-state; Simulation technique; Transition rule; Universal Turing machine;
Academic Unit:	Faculty of Science and Engineering > Computer Science Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	12415
Identification Number:	https://doi.org/10.3233/FI-2009-0039
Depositing User:	Damien Woods
Date Deposited:	13 Feb 2020 15:56
Journal or Publication Title:	Fundamenta Informaticae
Publisher:	IOS Press
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

Repository Staff Only(login required)

Item control page

Downloads

Origin of downloads