Introduction to algorithms
Randomized algorithms
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Extractors and pseudo-random generators with optimal seed length
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Deterministic Algorithms for k-SAT Based on Covering Codes and Local Search
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Filtering random noise from deterministic signals via datacompression
IEEE Transactions on Signal Processing
Covering codes with improved density
IEEE Transactions on Information Theory
Dimensions of Points in Self-similar Fractals
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Randomness, computation and mathematics
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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We introduce the study of Kolmogorov complexity with error. For a metric d, we define Ca(x) to be the length of a shortest program p which prints a string y such that d(x,y) ≤ a. We also study a conditional version of this measure Ca, b(x|y) where the task is, given a string y′ such that d(y,y′) ≤ b, print a string x′ such that d(x,x′) ≤ a. This definition admits both a uniform measure, where the same program should work given any y′ such that d(y,y′) ≤ b, and a nonuniform measure, where we take the length of a program for the worst case y′. We study the relation of these measures in the case where d is Hamming distance, and show an example where the uniform measure is exponentially larger than the nonuniform one. We also show an example where symmetry of information does not hold for complexity with error under either notion of conditional complexity.