Electronic Colloquium on Computational Complexity, Report No. 54 (2005) Time Hierarchies for Computations with a Bit of Advice

A polynomial time hierarchy for ZPTime with one bit of advice is proved. That is for any constants a and b such that 1 < a < b, ZPTime[n a]/1 � ZPTime[n b]/1. The technique introduced in this paper is very general and gives the same hierarchy for NTime∩coNTime, UTime, MATime, AMTime and BQTime. It also significantly simplifies the previously known proofs of hierarchies for BPTime and RPTime with advice.