A Pseudorandum Oracle Characterization of BBP

Every language that is polynomial time many-one hard for ESPACE is shown to have unusually small complexity cores and unusually low space-bounded Kolmogorov complexity. It follows that the polynomial time many-one complete languages form a measure 0 subset of ESPACE

Lines Missing Every Random Point

We prove that there is, in every direction in Euclidean space, a line that misses every computably random point. We also prove that there exist, in every direction in Euclidean space, arbitrarily long line segments missing every double exponential time random point.Comment: Added a section: "Betting in Doubly Exponential Time.

Resource-bounded Measure on Probabilistic Classes

We extend Lutz’s resource-bounded measure to probabilistic classes, and obtain notions of resource-bounded measure on probabilistic complexity classes such as BPE and BPEXP. Unlike former attempts, our resource bounded measure notions satisfy all three basic measure properties, that is every singleton {L} has measure zero, the whole space has measure one, and "enumerable infinite unions" of measure zero sets have measure zero

Resource-bounded Measure on Probabilistic Classes

We extend Lutz’s resource-bounded measure to probabilistic classes, and obtain notions of resource-bounded measure on probabilistic complexity classes such as BPE and BPEXP. Unlike former attempts, our resource bounded measure notions satisfy all three basic measure properties, that is every singleton {L} has measure zero, the whole space has measure one, and "enumerable infinite unions" of measure zero sets have measure zero

A zero-one SUBEXP-dimension law for BPP

We show that BPP has either SUBEXP-dimension zero (randomness is easy) or BPP=EXP (randomness is intractable).Comment: to be published in information processing letter