Algorithmic information theory
Algorithmic information theory
Information randomness & incompleteness: papers on algorithmic information theory (2nd ed.)
Information randomness & incompleteness: papers on algorithmic information theory (2nd ed.)
LISP program-size complexity IV
Applied Mathematics and Computation
Kolmogorov complexity and Hausdorff dimension
Information and Computation
Cornerstones of undecidability
Cornerstones of undecidability
On the Length of Programs for Computing Finite Binary Sequences
Journal of the ACM (JACM)
A Theory of Program Size Formally Identical to Information Theory
Journal of the ACM (JACM)
Recursively enumerable reals and Chaitin &OHgr; numbers
Theoretical Computer Science
Information and Randomness: An Algorithmic Perspective
Information and Randomness: An Algorithmic Perspective
Randomness and Recursive Enumerability
SIAM Journal on Computing
The Kolmogorov complexity of real numbers
Theoretical Computer Science
The dimensions of individual strings and sequences
Information and Computation
Visualization 2001 Conference (Acm
Visualization 2001 Conference (Acm
Very Simple Chaitin Machines for Concrete AIT
Fundamenta Informaticae
Fixed Point Theorems on Partial Randomness
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
On universal computably enumerable prefix codes
Mathematical Structures in Computer Science
Information: The Algorithmic Paradigm
Formal Theories of Information
Infinities in quantum field theory and in classical computing: renormalization program
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Quantum query algorithms for conjunctions
UC'10 Proceedings of the 9th international conference on Unconventional computation
A Chaitin $$\Upomega$$ number based on compressible strings
Natural Computing: an international journal
Phase transition between unidirectionality and bidirectionality
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
Introduction: computability of the physical
Mathematical Structures in Computer Science
Renormalisation and computation ii: Time cut-off and the halting problem
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science
| Hi-index | 0.00 |
We introduce the zeta number, natural halting probability, and natural complexity of a Turing machine and we relate them to Chaitin's Omega number, halting probability, and program-size complexity. A classification of Turing machines according to their zeta numbers is proposed: divergent, convergent, and tuatara. We prove the existence of universal convergent and tuatara machines. Various results on (algorithmic) randomness and partial randomness are proved. For example, we show that the zeta number of a universal tuatara machine is c.e. and random. A new type of partial randomness, asymptotic randomness, is introduced. Finally we show that in contrast to classical (algorithmic) randomness--which cannot be naturally characterised in terms of plain complexity--asymptotic randomness admits such a characterisation.