On the random oracle hypothesis
Information and Control
Information-theoretic incompleteness
Information-theoretic incompleteness
Hilbert's tenth problem
The random oracle hypothesis is false
Journal of Computer and System Sciences
Applied Mathematics and Computation
A Theory of Program Size Formally Identical to Information Theory
Journal of the ACM (JACM)
Quantum mechanics and algorithmic randomness
Complexity
A new kind of science
The Universal Computer: The Road from Leibniz to Turing
The Universal Computer: The Road from Leibniz to Turing
Information and Randomness: An Algorithmic Perspective
Information and Randomness: An Algorithmic Perspective
Coins, Quantum Measurements, and Turing's Barrier
Quantum Information Processing
Chaitin Ω numbers, Solovay machines, and Gödel incompleteness
Theoretical Computer Science
Meta Math!: The Quest for Omega
Meta Math!: The Quest for Omega
Visualization 2001 Conference (Acm
Visualization 2001 Conference (Acm
Riemann's hypothesis and tests for primality
Journal of Computer and System Sciences
Oracles and Advice as Measurements
UC '08 Proceedings of the 7th international conference on Unconventional Computing
Mathematics, metaphysics and the multiverse
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
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Is randomness in quantum mechanics “algorithmically random”? Is there any relation between Heisenberg's uncertainty relation and Gödel's incompleteness? Can quantum randomness be used to trespass the Turing's barrier? Can complexity shed more light on incompleteness? In this paper we use variants of “algorithmic complexity” to discuss the above questions.