Some hierarchies of relativized time-bounded complexity classes

Hierarchies of Relativized Time - Bounded

Some results on relativized time-bounded complexity classes are presented. There can be many kinds of hierarchies of complexity subclasses of relativized NP. For brevity, let P(A, k) \NP(A, k)} be the relativized complexity class DTIME^(/i*) [resp. NTIME^/i*)] with respect to oracle set A. (For k=l, replace n by 2ri). Then for example: 1). There is an oracle set A such that for all k>Q P(A, k) ...

Some Results on Relativized Deterministic and Nondeterministic Time Hierarchies

Relativized forms of deterministic and nondeterministic time complexity classes are considered. It is shown, at variance with recently published observations, that one basic step by step simulation technique in complexity theory does not relativize (i.e., does not generalize to computations with oracles), using the current definitions for time and space complexity of oracle computations. A new ...

Relativized Separation of Reversible and Irreversible Space-Time Complexity Classes

Reversible computing can reduce the energy dissipation of computation, which can improve cost-efficiency in some contexts. But the practical applicability of this method depends sensitively on the space and time overhead required by reversible algorithms. Time and space complexity classes for reversible machines match conventional ones, but we conjecture that the joint space-time complexity cla...

Relativized Separation of Reversible and Irreversible Space-Time Complexity Classes

Circuit Lower Bounds Collapse Relativized Complexity Classes

Since the publication of Furst, Saxe, and Sipser's seminal paper connecting AC 0 with the polynomial hierarchy FSS84], it has been well known that circuit lower bounds allow you to construct oracles that separate complexity classes. We will show that similar circuit lower bounds allow you to construct oracles that collapse complexity classes. For example, based on H astad's parity lower bound, ...