Four Small Universal Turing Machines

Four Small Universal Turing Machines (2009)

Cached

Download Links

by Turlough Neary , Damien Woods

Citations:

BibTeX

@MISC{Neary09foursmall,
    author = {Turlough Neary and Damien Woods},
    title = { Four Small Universal Turing Machines},
    year = {2009}
}

Bookmark

OpenURL

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-symbol machine uses the same number of instructions (22) as the smallest known universal Turing machine by Rogozhin. Also, all of the universal machines we present here simulate Turing machines in polynomial time.

Citations

352	Computation: Finite and Infinite Machines - Minsky - 1967
46	Universality in elementary cellular automata - Cook - 2004
24	Small universal Turing machines - Rogozhin - 1996
23	A universal Turing machine with two internal states - Shannon - 1956
17	Three small universal Turing machines - Baiocchi - 2001
16	Universality of tag systems with P = 2 - Cocke, Minsky - 1964
16	Size and structure of universal Turing machines using Tag systems - Minsky - 1962
14	Small fast universal Turing machines - Neary, Woods - 2006
13	On the time complexity of 2-tag systems and small universal turing machines - Neary, Woods - 2006
10	The uniform halting problem for generalized one state Turing machines - Hermann - 1968
9	Small deterministic Turing machines - Kudlek - 1996
9	A universal Turing machine with 3 states and 9 symbols - Kudlek, Rogozhin - 2002
8	Solvability of the halting problem for certain classes of Turing machines - Pavlotskaya - 1973
8	Dostatochnye uslovija razreshimosti problemy ostanovki dlja mashin T’juring. Problemi kibernetiki - Pavlotskaya - 1978
8	Minsky's small universal Turing machine - Robinson - 1991
8	Small semi-weakly universal Turing machines - Woods, Neary - 2009
7	The complexity of small universal Turing machines - Woods, Neary
6	On the optimal number of instructions for universality of Turing machines connected with a finite automaton - Margenstern, Pavlotskaya - 2003
6	polynomial time universal Turing machines - Small
5	Small weakly universal Turing machines - Neary, Woods - 2007
3	On quasi-unilateral universal Turing machines - Margenstern - 2001
2	Small universal circular Post machines - Kudlek, Rogozhin
2	Frontier between decidablity and undecidablity: a survey - Margenstern - 2000