A Theory of Program Size Formally Identical to Information Theory
Journal of the ACM (JACM)
Information and Randomness: An Algorithmic Perspective
Information and Randomness: An Algorithmic Perspective
The Universal Turing Machine: A Half-Century Survey
The Universal Turing Machine: A Half-Century Survey
Randomness and Recursive Enumerability
SIAM Journal on Computing
Chaitin Ω numbers, Solovay machines, and Gödel incompleteness
Theoretical Computer Science
Recursively Enumerable Reals and Chaitin Omega Numbers
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Visualization 2001 Conference (Acm
Visualization 2001 Conference (Acm
The Complexity of Small Universal Turing Machines
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Universal Recursively Enumerable Sets of Strings
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
On universal computably enumerable prefix codes
Mathematical Structures in Computer Science
Computability and Randomness
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
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
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Universality, provability and simplicity are key notions in computability theory. There are various criteria of simplicity for universal Turing machines. Probably the most popular one is to count the number of states/symbols. This criterion is more complex than it may appear at a first glance. In this note we propose three new criteria of simplicity for universal prefix-free Turing machines. These criteria refer to the possibility of proving various natural properties of such a machine (its universality, for example) in a formal theory, Peano arithmetic or Zermelo-Fraenkel set theory. In all cases some, but not all, machines are simple.