On the Length of Programs for Computing Finite Binary Sequences
Journal of the ACM (JACM)
A Theory of Program Size Formally Identical to Information Theory
Journal of the ACM (JACM)
Proceedings on Mathematical Foundations of Computer Science
The Kolmogorov complexity of real numbers
Theoretical Computer Science
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Gales and the Constructive Dimension of Individual Sequences
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
The Kolmogorov Complexity of Real Numbers
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
The dimensions of individual strings and sequences
Information and Computation
Theoretical Computer Science
Constructive dimension equals Kolmogorov complexity
Information Processing Letters
SIGACT news complexity theory column 48
ACM SIGACT News
The Kolmogorov complexity of infinite words
Theoretical Computer Science
Dimensions of Points in Self-similar Fractals
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Effective symbolic dynamics, random points, statistical behavior, complexity and entropy
Information and Computation
Constructive dimension equals Kolmogorov complexity
Information Processing Letters
On the Kolmogorov complexity of continuous real functions
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
Kolmogorov-Loveland randomness and stochasticity
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
A correspondence principle for exact constructive dimension
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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We investigate the Kolmogorov complexity of real numbers. Let K be the Kolmogorov complexity function; we determine the Hausdorff dimension and the topological dimension of the graph of K. Since these dimensions are different, the graph of the Kolmogorov complexity function of the real line forms a fractal in the sense of Mandelbrot. We also solve an open problem of Razborov using our exact bound on the topological dimension.