Elementary differences between the degrees of unsolvability and degrees of compressibility
نویسندگان
چکیده
منابع مشابه
Elementary differences between the degrees of unsolvability and degrees of compressibility
Given two infinite binary sequences A, B we say that B can compress at least as well as A if the prefix-free Kolmogorov complexity relative to B of any binary string is at most as much as the prefix-free Kolmogorov complexity relative to A, modulo a constant. This relation, introduced in Nies (2005) [14] and denoted by A≤LK B, is a measure of relative compressing power of oracles, in the same w...
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Modern computability theory began with Turing [Turing, 1936], where he introduced the notion of a function computable by a Turing machine. Soon after, it was shown that this definition was equivalent to several others that had been proposed previously and the Church-Turing thesis that Turing computability captured precisely the informal notion of computability was commonly accepted. This isolat...
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Computable analysis provides a standard notion of computability for continuous functions on the real numbers. This notion was first explicitly formulated and studied by Lacombe and Grzegorczyk in the 1950’s, although it can be traced back to Turing and beyond that to Brouwer. However, a satisfactory notion of the degrees of unsolvability of continuous functions has only recently been introduced...
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Recall that RT is the upper semilattice of recursively enumerable Turing degrees. We consider two fundamental, classical, unresolved issues concerning RT . The first issue is to find a specific, natural, recursively enumerable Turing degree a ∈ RT which is > 0 and < 0 ′. The second issue is to find a “smallness property” of an infinite, co-recursively enumerable set A ⊆ ω which ensures that the...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2010
ISSN: 0168-0072
DOI: 10.1016/j.apal.2009.11.004