Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
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
Proceedings of the workshop on Lattice dynamics
5-Symbol 8-State and 5-Symbol 6-State Universal Turing Machines
Journal of the ACM (JACM)
Universality of Tag Systems with P = 2
Journal of the ACM (JACM)
Frontier between decidability and undecidability: a survey
Theoretical Computer Science - Special issue on universal machines and computations
Nine switch-affine neurons suffice for turing universality
Neural Networks
The Quest for Small Universal Cellular Automata
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Non-Erasing Turing Machines: A New Frontier Between a Decidable Halting Problem and Universality
LATIN '95 Proceedings of the Second Latin American Symposium on Theoretical Informatics
A Universal Turing Machine with 3 States and 9 Symbols
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
Non Erasing Turing Machines: A Frontier Between a Decidable Halting Problem and Universality
FCT '93 Proceedings of the 9th International Symposium on Fundamentals of Computation 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
Automata Studies. (AM-34) (Annals of Mathematics Studies)
Automata Studies. (AM-34) (Annals of Mathematics Studies)
Cellular Automata
On the time complexity of 2-tag systems and small universal Turing machines
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
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)
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
Quantum Information & Computation
On the rule complexity of universal tissue p systems
WMC'05 Proceedings of the 6th international conference on Membrane Computing
P-completeness of cellular automaton rule 110
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Splicing systems for universal turing machines
DNA'04 Proceedings of the 10th international conference on DNA computing
Simplicity via provability for universal prefix-free Turing machines
Theoretical Computer Science
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We survey some work concerned with small universal Turing machines, cellular automata, and other simple models of computation. For example it has been an open question for some time as to whether the smallest known universal Turing machines of Minsky, Rogozhin, Baiocchi and Kudlek are efficient (polynomial time) simulators of Turing machines. These are some of the most intuitively simple computational devices and previously the best known simulations were exponentially slow. We discuss recent work that shows that these machines are indeed efficient simulators. As a related result we also find that Rule 110, a well-known elementary cellular automaton, is also efficiently universal. We also mention some new universal program-size results, including new small universal Turing machines and new semi-weakly universal Turing machines. We then discuss some ideas for future work arising out of these, and other, results.