Promise Hierarchies

We show that for any constant a, ZPP/b(n) strictly contains ZPTIME(n)/b(n) for some b(n) = O(log n log log n). Our techniques are very general and give the same hierarchy for all the common promise time classes including RTIME, NTIME ∩ coNTIME, UTIME, MATIME, AMTIME and BQTIME. We show a stronger hierarchy for RTIME: For every constant c, RP/1 is not contained in RTIME(n)/(log n). To prove this result we first prove a similar statement for NP by building on Žák’s proof of the nondeterministic time hierarchy.