Small universal Turing machines
Theoretical Computer Science - Special issue on universal machines and computations
Small deterministic Turing machines
Theoretical Computer Science - Special issue on universal machines and computations
On machines, universal by extensions
Theoretical Computer Science - Special issue on universal machines and computations
5-Symbol 8-State and 5-Symbol 6-State Universal Turing Machines
Journal of the ACM (JACM)
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Journal of the ACM (JACM)
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Theoretical Computer Science - Special issue on universal machines and computations
A new kind of science
A Universal Turing Machine with 3 States and 9 Symbols
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
Three Small Universal Turing Machines
MCU '01 Proceedings of the Third International Conference on Machines, Computations, and Universality
Small turing machines and generalized busy beaver competition
Theoretical Computer Science
On the time complexity of 2-tag systems and small universal Turing machines
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Small fast universal turing machines
Theoretical Computer Science
The uniform halting problem for generalized one state turing machines
SWAT '68 Proceedings of the 9th Annual Symposium on Switching and Automata Theory (swat 1968)
The complexity of small universal Turing machines: A survey
Theoretical Computer Science
Four Small Universal Turing Machines
Fundamenta Informaticae - Machines, Computations and Universality, Part I
Four small universal turing machines
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
Small semi-weakly universal turing machines
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
P-completeness of cellular automaton rule 110
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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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 can be regarded as a continuation of early work by Watanabe on semi-weak machines. One of our machines has only 17 transition rules, making it the smallest known semi-weakly universal Turing machine. Interestingly, two of our machines are symmetric with Watanabe's 7-state and 3-symbol, and 5-state and 4-symbol machines, even though we use a different simulation technique.