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]/1 ( ZPTime[n]/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 ad...

One of the important questions Christian geography was location Paradise on inhabited Earth. Among various theories provided by authorities, none is as sophisticated that Philostorgius. Philostorgius put forward proposition located in eastern part world, equator, with a demonstration largely based classical non-Christian paideia.

We characterize the collapse of Buss' bounded arithmetic in terms of the provable collapse of the polynomial time hierarchy. We include also some general model-theoretical investigations on fragments of bounded arithmetic.