Fixed point theorems on partial randomness

DOI10.1016/j.apal.2011.09.018zbMath1247.03088OpenAlexW2949413845MaRDI QIDQ408531

Kohtaro Tadaki

Publication date: 10 April 2012

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2011.09.018

zbMATH Keywords

algorithmic information theoryfixed-point theoremthermodynamic quantitiesalgorithmic randomnesspartial randomnessChaitin \(\Omega \) number

Mathematics Subject Classification ID

Algorithmic information theory (Kolmogorov complexity, etc.) (68Q30) Foundations of equilibrium statistical mechanics (82B03) Algorithmic randomness and dimension (03D32)

Related Items (2)

A statistical mechanical interpretation of algorithmic information theory III: composite systems and fixed points ⋮ Algorithmic information theory and its statistical mechanical interpretation

Cites Work

• Natural halting probabilities, partial randomness, and zeta functions
• Effectively closed sets of measures and randomness
• Infinite subsets of random sets of integers
• Incompleteness theorems for random reals
• Statistical physics I. Equilibrium statistical mechanics. Rev. transl. from the Japanese ed. by Morikazu Toda and Nobuhiko Saitô.
• A generalization of Chaitin's halting probability \(\Omega\) and halting self-similar sets
• On partial randomness
• Algorithmic Randomness and Complexity
• A Theory of Program Size Formally Identical to Information Theory
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