Online Computability and Differentiation in the Cantor Space

Cenzer, Douglas; Rojas, Diego A.

doi:10.1007/978-3-319-94418-0_14

Cited by 5 publications

(3 citation statements)

References 12 publications

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“…Recalling that our Bernoulli parameters are p 0 = q, p 1 = r and p 2 = s, we first consider the case when s = 0. These corresponding µ-random functionals are the so-called online random functionals from [3,5]. We will assume without loss of generality that q ≤ r < 1.…”

Section: Ratementioning

confidence: 99%

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Extraction Rates of Algorithmically Random Continuous Functionals

Cenzer,

Fraize,

Porter

2023

Preprint

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In this article, we study the extraction rate, or output/input rate, of continuous functionals on the Cantor space 2ω, in particular for algorithmically random functionals. It is shown that random functionals have an average extraction rate over all inputs corresponding to the rate of producing a single bit of output, and that this average rate is attained for any sufficiently random input. We also examine functions computed by discrete distribution generating trees, where we calculate the expected extraction rate and show that this rate is attained for any sufficiently random input.

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Section: Ratementioning

confidence: 99%

“…The online computable functions are an interesting class, and were studied by Cenzer and Porter [3] and by Cenzer and Rojas [5].…”

Section: Introductionmentioning

confidence: 99%

Extraction Rates of Algorithmically Random Continuous Functionals

Cenzer,

Fraize,

Porter

2023

Preprint

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“…The authors have studied some families of functions for which this is the case. First, there are the so-called online continuous (or computable) functions, which compute exactly one bit of output for each bit of input (see [CR18]). On the other hand, there are the random continuous functions which produce regularity in a probabilistic sense.…”

Section: 3mentioning

confidence: 99%

Randomness extraction in computability theory

Cenzer¹,

Porter²

2021

Preprint

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In this article, we study a notion of the extraction rate of Turing functionals that translate between notions of randomness with respect to different underlying probability measures. We analyze several classes 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 from unbiased randomness by Knuth and Yao, and a third class independently developed by Levin and Kautz that generalizes the data compression technique of arithmetic coding. For the first two classes of extraction procedures, we identify a level of algorithmic randomness for an input that guarantees that we attain the extraction rate along that input, while for the third class, we calculate the rate attained along sufficiently random input sequences.

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