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.)
A Theory of Program Size Formally Identical to Information Theory
Journal of the ACM (JACM)
The unknowable
Recursively enumerable reals and Chaitin &OHgr; numbers
Theoretical Computer Science
Information and Randomness: An Algorithmic Perspective
Information and Randomness: An Algorithmic Perspective
A characterization of c.e. random reals
Theoretical Computer Science
Randomness and Recursive Enumerability
SIAM Journal on Computing
Randomness as an Invariant for Number Representations
Proceedings of the Colloquium in Honor of Arto Salomaa on Results and Trends in Theoretical Computer Science
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Incompleteness, Complexity, Randomness and Beyond
Minds and Machines
Information: The Algorithmic Paradigm
Formal Theories of Information
Simplicity via provability for universal prefix-free Turing machines
Theoretical Computer Science
Algorithmic randomness, quantum physics, and incompleteness
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
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Computably enumerable (c.e.) reals can be coded by Chaitin machines through their halting probabilities. Tuning Solovay's construction of a Chaitin universal machine for which ZFC (if arithmetically sound) cannot determine any single bit of the binary expansion of its halting probability, we show that every c.e. random real is the halting probability of a universal Chaitin machine for which ZFC cannot determine more than its initial block of 1 bits-as soon as you get a 0, it is all over. Finally, a constructive version of Chaitin information-theoretic incompleteness theorem is proven.