eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-08-19
86:1
86:13
10.4230/LIPIcs.MFCS.2016.86
article
Polynomial Space Randomness in Analysis
Huang, Xiang
Stull, Donald M.
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol058-mfcs2016/LIPIcs.MFCS.2016.86/LIPIcs.MFCS.2016.86.pdf
algorithmic randomness
computable analysis
resource-bounded randomness
complexity theory