Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
A Theory of Program Size Formally Identical to Information Theory
Journal of the ACM (JACM)
The unknowable
Information and Randomness: An Algorithmic Perspective
Information and Randomness: An Algorithmic Perspective
Information, Randomness and Incompleteness
Information, Randomness and Incompleteness
Program-Size Complexity of Initial Segments and Domination Reducibility
Jewels are Forever, Contributions on Theoretical Computer Science in Honor of Arto Salomaa
Randomness as an Invariant for Number Representations
Proceedings of the Colloquium in Honor of Arto Salomaa on Results and Trends in Theoretical Computer Science
Recursively Enumerable Reals and Chaitin Omega Numbers
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Chaitin Ω numbers, Solovay machines, and Gödel incompleteness
Theoretical Computer Science
The closure properties on real numbers under limits and computable operators
Theoretical Computer Science
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
On the Construction of Effective Random Sets
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Randomness, Computability, and Density
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
On the hierarchy and extension of monotonically computable real numbers
Journal of Complexity
On the existence of a new family of Diophantine equations for Ω
Fundamenta Informaticae
Journal of Computer and System Sciences
Divergence bounded computable real numbers
Theoretical Computer Science - Real numbers and computers
Another Example of Higher Order Randomness
Fundamenta Informaticae
On the divergence bounded computable real numbers
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
On the monotonic computability of semi-computable real numbers
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
On the existence of a new family of Diophantine equations for Ω
Fundamenta Informaticae
Another Example of Higher Order Randomness
Fundamenta Informaticae
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A real α is computably enumerable if it is the limit of a computable, increasing, converging sequence of rationals. A real α is random if its binary expansion is a random sequence. Our aim is to offer a self-contained proof, based on the papers (Calude et al., in: M. Morvan, C. Meinel, D. Krob (Eds.), Proc. 15th Symp. on Theoretical Aspects of Computer Science, Paris, Springer, Berlin, 1998, pp. 596-606; Chaitin, J. Assoc. Comput. Mach. 22 (1975) 329; Slaman, manuscript, 14 December 1998, 2 pp.; Solovay, unpublished manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, New York, May 1975, 215 pp.), of the following theorem: a real is c.e. and random if and only if it is a Chaitin&Ohgr; real, i.e., the halting probability of some universal self-delimiting Turing machine.