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Complexity of Small Universal Turing Machines: A Survey

Neary, Turlough and Woods, Damien (2012) Complexity of Small Universal Turing Machines: A Survey. In: SOFSEM 2012: Theory and Practice of Computer Science. Lecture Notes in Computer Science. No.7147. Springer , Berlin, pp. 385-405. ISBN 978-3-642-27659-0. https://resolver.caltech.edu/CaltechAUTHORS:20200520-110921412

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Abstract

We survey some work concerned with small universal Turing machines, cellular automata, tag systems, and other simple models of computation. For example it has been an open question for some time as to whether the smallest known universal Turing machines of Minsky, Rogozhin, Baiocchi and Kudlek are efficient (polynomial time) simulators of Turing machines. These are some of the most intuitively simple computational devices and previously the best known simulations were exponentially slow. We discuss recent work that shows that these machines are indeed efficient simulators. In addition, another related result shows that Rule 110, a well-known elementary cellular automaton, is efficiently universal. We also discuss some old and new universal program size results, including the smallest known universal Turing machines. We finish the survey with results on generalised and restricted Turing machine models including machines with a periodic background on the tape (instead of a blank symbol), multiple tapes, multiple dimensions, and machines that never write to their tape. We then discuss some ideas for future work.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/978-3-642-27660-6_32DOIArticle
https://rdcu.be/b4iHlPublisherFree ReadCube access
https://arxiv.org/abs/1110.2230arXivDiscussion Paper
Additional Information:© 2012 Springer-Verlag Berlin Heidelberg. This paper is extended and updated from [110]. T. Neary is supported by Science Foundation Ireland, Grant Number 09/RFP/CMS2212. D. Woods is supported by National Science Foundation Grant 0832824, the Molecular Programming Project. We thank Astrid Haberleitner for her tireless work in translating a number of highly technical papers from German to English, and Beverley Henley for her support.
Funders:
Funding AgencyGrant Number
Science Foundation, Ireland09/RFP/CMS2212
NSFCCF-0832824
Subject Keywords:Cellular Automaton; Turing Machine; Transition Rule; Time Overhead; Program Size
Series Name:Lecture Notes in Computer Science
Issue or Number:7147
DOI:10.1007/978-3-642-27660-6_32
Record Number:CaltechAUTHORS:20200520-110921412
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200520-110921412
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103354
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 May 2020 18:18
Last Modified:16 Nov 2021 18:20

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