Four Small Universal Turing Machines

Authors:
Turlough Neary;Damien Woods
Affiliations:
(Correspd.) Boole Centre for Research in Informatics, University College Cork, Ireland. tneary@cs.nuim.ie;Department of Computer Science and Artificial Intelligence, University of Seville, Spain. d.woods@cs.ucc.ie
Venue:
Fundamenta Informaticae - Machines, Computations and Universality, Part I
Year:
2009

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Abstract

We present universal Turing machines with state-symbol pairs of (5, 5), (6, 4), (9, 3) and (15, 2). These machines simulate our new variant of tag system, the bi-tag system and are the smallest known single-tape universal Turing machines with 5, 4, 3 and 2-symbols, respectively. Our 5-symbolmachine uses the same number of instructions (22) as the smallest known universal Turing machine by Rogozhin. Also, all of the universalmachines we present here simulate Turing machines in polynomial time.