Abstract Geometrical Computation and Computable Analysis

We examine a construction due to Fouché in which a Brownian motion is constructed from an algorithmically random infinite binary sequence. We show that although the construction is provably not computable in the sense of computable analysis, a lower bound for the rate of convergence is computable in any upper bound for the compressibilty of the sequence, making the construction layerwise computable.

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A foundation for computable analysis

Foundations of Computer Science - Lecture Notes in Computer Science ◽

10.1007/bfb0052087 ◽

1997 ◽

pp. 185-199 ◽

Cited By ~ 5

Author(s):

Klaus Weihrauch

Keyword(s):

Computable Analysis

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Further Topics in Computable Analysis

Computability in Analysis and Physics ◽

10.1017/9781316717325.007 ◽

2017 ◽

pp. 50-74

Author(s):

Marian B. Pour-El ◽

J. Ian Richards

Keyword(s):

Computable Analysis

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Absolutely Non-effective Predicates and Functions in Computable Analysis

Lecture Notes in Computer Science - Theory and Applications of Models of Computation ◽

10.1007/978-3-540-72504-6_54 ◽

2007 ◽

pp. 595-604 ◽

Cited By ~ 1

Author(s):

Decheng Ding ◽

Klaus Weihrauch ◽

Yongcheng Wu

Keyword(s):

Computable Analysis

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Signal Recovery by Linear Estimation

Statistical Inference via Convex Optimization ◽

10.23943/princeton/9780691197296.003.0004 ◽

2019 ◽

pp. 260-385

Author(s):

John Stillwell

Keyword(s):

Human Activities ◽

Mathematical Concept ◽

Rational Numbers ◽

Precise Definition ◽

Computable Analysis ◽

Signal Recovery ◽

Linear Estimation ◽

Definition Of ◽

Computable Sequence ◽

Informal Description

This chapter develops the basic results of computability theory, many of which are about noncomputable sequences and sets, with the goal of revealing the limits of computable analysis. Two of the key examples are a bounded computable sequence of rational numbers whose limit is not computable, and a computable tree with no computable infinite path. Computability is an unusual mathematical concept, because it is most easily used in an informal way. One often talks about it in terms of human activities, such as making lists, rather than by applying a precise definition. Nevertheless, there is a precise definition of computability, so this informal description of computations can be formalized.

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