Deterministic k-tape and multitape Turing machines with one-way, two-way and without a separated input tape are considered. We investigate the classes of languages acceptable by such devices with time bounds of the form n+r(n) where r in o(n) is a sublinear function. It is shown that there exist infinite time ... more >>>

Building on Barak's work (Random'02), Fortnow and Santhanam (FOCS'04) proved a time hierarchy for probabilistic machines with one bit of advice. Their argument is based on an implicit translation technique, which allow to translate separation results for short (say logarithmic) advice (as shown by Barak) into separations for a single-bit ... more >>>

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 \subsetneq ZPTime[n^b]/1. The technique introduced in this paper is very general and gives the same hierarchy for NTime \cap coNTime, UTime, ... more >>>

We survey time hierarchies, with an emphasis on recent attempts to prove hierarchies for semantic classes. more >>>