Logical depth and physical complexity
A half-century survey on The Universal Turing Machine
Almost everywhere high nonuniform complexity
Journal of Computer and System Sciences
Computational depth and reducibility
Theoretical Computer Science
On encoding and decoding with two-way head machines
Information and Computation
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
The quantitative structure of exponential time
Complexity theory retrospective II
Information and Computation
Switching and Finite Automata Theory: Computer Science Series
Switching and Finite Automata Theory: Computer Science Series
Note: fractal dimension and logarithmic loss unpredictability
Theoretical Computer Science
Theoretical Computer Science
Computational depth: concept and applications
Theoretical Computer Science - Foundations of computation theory (FCT 2003)
Entropy rates and finite-state dimension
Theoretical Computer Science
Effective Strong Dimension in Algorithmic Information and Computational Complexity
SIAM Journal on Computing
Information and Computation
On the polynomial depth of various sets of random strings
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Theoretical Computer Science
On the polynomial depth of various sets of random strings
Theoretical Computer Science
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This paper introduces two complexity-theoretic formulations of Bennett's logical depth: finite-state depthand polynomial-time depth. It is shown that for both formulations, trivial and random infinite sequences are shallow, and a slow growth lawholds, implying that deep sequences cannot be created easily from shallow sequences. Furthermore, the Eanalogue of the halting language is shown to be polynomial-time deep, by proving a more general result: every language to which a nonnegligible subset of Ecan be reduced in uniform exponential time is polynomial-time deep.