Observations on complete sets between linear time and polynomial time
There is a single set that is complete for a variety of nondeterministic time complexity classes with respect to related versions of m-reducibility. This observation immediately leads to transfer results for determinism versus nondeterminism solutions. Also, an upward transfer of collapses of certain oracle hierarchies, built analogously to the polynomial-time or the linear-time hierarchies, can be shown by means of uniformly constructed sets that are complete for related levels of all these hierarchies. A similar result holds for difference hierarchies over nondeterministic complexity classes. Finally, we give an oracle set relative to which the nondeterministic classes coincide with the deterministic ones, for several sets of time bounds, and we prove that the strictness of the tape-number hierarchy for deterministic linear-time Turing machines does not relativize. (C) 2010 Elsevier Inc. All rights reserved.
completeness determinism versus nondeterminism linear-time hierarchy many-one reducibility polynomial-time hierarchy boolean hierarchy