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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)
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)
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)
Acknowledgements My supervisor Damien Woods deserves a special thank you. His help and guidance went far beyond the role of supervisor. He was always enthusiastic, and generous with his time. This work would not have happened without him. I would also like to thank my supervisor Paul Gibson for his advice and support. Thanks to the staff and postgraduates(More)
In this work we offer a significant improvement on the previous smallest spiking neural P system. P˘ aun and P˘ aun [3] gave a universal spiking neural P system with 84 neurons. Subsequently, Zhang et al. [18] reduced the number of neurons used to give universality to 67. Here we give a small universal spiking neural P system that has only 11 neurons and(More)