Languages to diagonalize against advice classes

Variants of Kannan's Theorem are given where the circuits of the original theorem are replaced by arbitrary recursively presentable classes of languages that use advice strings and satisfy certain mild conditions. Let polyk denote those functions in O(nk). These variants imply that DTIME(nk )NE/polyk does not contain PNE, DTIME(2nk )/polyk does not contain EXP, SPACE(nk )/polyk does not contain PSPACE, uniform TC0 /polyk does not contain CH, and uniform ACC/polyk does not contain ModPH. Consequences for selective sets are also obtained. In particular, it is shown that R DTIME(nk) T (NP-sel) does not contain PNE, R DTIME(nk) T (P-sel) does not contain EXP, and that R DTIME(nk) T (L-sel) does not contain PSPACE. Finally, a circuit size hierarchy theorem is established. Keywords. advice classes, EXP, NEXP, NE, CH, ModPH, p-selective

• Type: Journal
• Year: 2006
• Where: CC
• Authors: Chris Pollett
• Keywords: Advice Strings, CC 2006, Certain Mild Conditions, Original Theorem, System Software