Kolmogorov complexity and Hausdorff dimension
Information and Computation
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Automata, Languages, and Machines
Automata, Languages, and Machines
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
The Complexity of Membership Problems for Circuits over Sets of Natural Numbers
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
On the entropy of a formal language
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Dimension in Complexity Classes
SIAM Journal on Computing
The dimensions of individual strings and sequences
Information and Computation
Theoretical Computer Science
Self-Affine Carpets on the Square Lattice
Combinatorics, Probability and Computing
Effective fractal dimension: foundations and applications
Effective fractal dimension: foundations and applications
Effective Strong Dimension in Algorithmic Information and Computational Complexity
SIAM Journal on Computing
Dimensions of Copeland--Erdös sequences
Information and Computation
Strict self-assembly of discrete Sierpinski triangles
Theoretical Computer Science
Self-assembly of discrete self-similar fractals
Natural Computing: an international journal
Complex network dimension and path counts
Theoretical Computer Science
Approximate self-assembly of the Sierpinski triangle
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Self-assembly of infinite structures: A survey
Theoretical Computer Science
Limitations of self-assembly at temperature 1
Theoretical Computer Science
Self-assembling rulers for approximating generalized sierpinski carpets
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Dimensions of copeland-erdös sequences
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
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The zeta-dimension of a set A of positive integers is Dimζ(A)=inf{s | ζA(s) where $\zeta_A(s)=\sum_{n\in A}n^{-s}.$ Zeta-dimension serves as a fractal dimension on ℤ+ that extends naturally and usefully to discrete lattices such as ℤd, where d is a positive integer. This paper reviews the origins of zeta-dimension (which date to the eighteenth and nineteenth centuries) and develops its basic theory, with particular attention to its relationship with algorithmic information theory. New results presented include a gale characterization of zeta-dimension and a theorem on the zeta-dimensions of pointwise sums and products of sets of positive integers.