Turlough Neary

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Yurii Rogozhin47
Marvin L. Minsky40
Matthew Cook39
John Cocke37
Manfred Kudlek35
32Damien Woods
20Dmitry A. Zaitsev
17Jérôme Olivier Durand-Lose
16Matthew Cook
10Maurice Margenstern

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2001
2017
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Four Small Universal Turing Machines
We present small polynomial time universal Turing machines with state-symbol pairs of (5, 5), (6, 4), (9, 3) and (18, 2). These machines simulate our new variant of tag system, the bi-tag system and are the smallest known universal Turing machines with 5, 4, 3 and 2-symbols respectively. Our 5-symbol machine uses the same number of instructions (22) as the… (More)
Small weakly universal Turing machines
We give small universal Turing machines with state-symbol pairs of (6, 2), (3, 3) and (2, 4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest known weakly universal Turing machines. Despite their small size… (More)
P-completeness of Cellular Automaton Rule 110
We show that the problem of predicting t steps of the 1D cellular automaton Rule 110 is P-complete. The result is found by showing that Rule 110 simulates deterministic Turing machines in polynomial time. As a corollary we find that the small universal Turing machines of Mathew Cook run in polynomial time, this is an exponential improvement on their… (More)
Small fast universal Turing machines
We present a number of time-efficient small universal Turing machines. We show that there exists deterministic polynomial time universal Turing machines with state-symbol products of (3, 11), (5, 7), (6, 6), (7, 5) and (8, 4). These machines are the smallest known universal Turing machines that simulate TMs in polynomial time.
Effects of androgens and estrogens and catechol and methoxy-estrogen derivatives on mitogen-activated protein kinase (ERK(1,2)) activity in SW-13 human adrenal carcinoma cells.
We tested the effects of 17beta-estradiol as well as its catechol- and methoxy-derivatives, two androgens (DHEA and testosterone), a glucocorticoid (cortisol), a mineralocorticoid (aldosterone), and progesterone on the activity of ERK(1,2), a key component of the ERK/MAPK enzyme phosphorylation cascade, in SW-13 human adrenal carcinoma cells. After a… (More)
On the time complexity of 2-tag systems and small universal Turing machines
We show that 2-tag systems efficiently simulate Turing machines. As a corollary we find that the small universal Turing machines of Rogozhin, Minsky and others simulate Turing machines in polynomial time. This is an exponential improvement on the previously known simulation time overhead and improves a forty year old result in the area of small universal… (More)
Small Semi-weakly Universal Turing Machines
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… (More)