Polynomial Space Randomness in Analysis
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.
algorithmic randomness
computable analysis
resource-bounded randomness
complexity theory
86:1-86:13
Regular Paper
Xiang
Huang
Xiang Huang
Donald M.
Stull
Donald M. Stull
10.4230/LIPIcs.MFCS.2016.86
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode