Journal Article10.1007/S00153-014-0378-7
Strict process machine complexity
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TL;DR: It is shown that for strict process machines, complexity of a sequence or of a subset of Cantor space is equal to its effective Hausdorff dimension.
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Abstract: We introduce a notion of description for infinite sequences and their sets, and a corresponding notion of complexity. We show that for strict process machines, complexity of a sequence or of a subset of Cantor space is equal to its effective Hausdorff dimension.
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Citations
•Posted Content
Randomness extraction in computability theory
TL;DR: In this paper, a notion of the extraction rate of Turing functionals that translate between notions of randomness with respect to different underlying probability measures is studied. But this work is restricted to the first class of extraction procedures: a first class that generalizes von Neumann's trick for extracting unbiased randomness from the tosses of a biased coin, a second class based on work of generating biased randomness by Knuth and Yao, and a third class independently developed by Levin and Kautz that generalises the data compression technique of arithmetic coding.
2
Randomness extraction in computability theory
19 Jan 2023
TL;DR: In this paper , a notion of the extraction rate of Turing functionals that translate between notions of randomness with respect to different underlying probability measures is studied. But this work is restricted to a class of extraction procedures: a class that generalizes von Neumann's trick for extracting unbiased randomness from the tosses of a biased coin, a class based on work of by Knuth and Yao, and a class independently developed by Levin and Kautz that generalises the data compression technique of arithmetic coding.
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TL;DR: It is shown that the random elements as defined by Kolmogorov possess all conceivable statistical properties of randomness and can equivalently be considered as the elements which withstand a certain universal stochasticity test.
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Algorithmic Randomness and Complexity
Rodney G. Downey,Denis R. Hirschfeldt +1 more
- 29 Oct 2010
TL;DR: This chapter discusses Randomness-Theoretic Weakness, Omega as an Operator, Complexity of C.E. Sets, and other Notions of Effective Randomness.
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The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms
A K Zvonkin,Leonid A. Levin +1 more
TL;DR: The present article is a survey of the fundamental results connected with the concept of complexity as the minimum number of binary signs containing all the information about a given object that are sufficient for its recovery (decoding).