Algorithmic information theory
Algorithmic information theory
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
Visualization 2001 Conference (Acm
Visualization 2001 Conference (Acm
Natural halting probabilities, partial randomness, and zeta functions
Information and Computation
Computability and Randomness
Chaitin Ω Numbers and Halting Problems
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Partial Randomness and Dimension of Recursively Enumerable Reals
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Representation of left-computable ε-random reals
Journal of Computer and System Sciences
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The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use function is explicitly specified. This elaboration enables us to deal with the notion of asymptotic behavior in a manner like in computational complexity theory, while staying in computability theory. We apply the elaboration to sets which appear in the statistical mechanical interpretation of algorithmic information theory. We demonstrate the power of the elaboration by revealing a critical phenomenon, i.e., a phase transition, in the statistical mechanical interpretation, which cannot be captured by the original notion of weak truth-table reducibility.