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Polynomial Space Randomness in Analysis

Authors Xiang Huang, Donald M. Stull

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LIPIcs.MFCS.2016.86.pdf
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Keywords
  • algorithmic randomness
  • computable analysis
  • resource-bounded randomness
  • complexity theory

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Abstract

We study the interaction between polynomial space randomness and a fundamental result of analysis, the Lebesgue differentiation theorem. We generalize Ko's framework for polynomial space computability in R^n to define weakly pspace-random points, a new variant of polynomial space randomness. We show that the Lebesgue differentiation theorem characterizes weakly pspace random points. That is, a point x is weakly pspace random if and only if the Lebesgue differentiation theorem holds for a point x for every pspace L_1-computable function.

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Xiang Huang and Donald M. Stull. Polynomial Space Randomness in Analysis. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 86:1-86:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.MFCS.2016.86

Author Details

Xiang Huang
Donald M. Stull
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