Bi-Immunity Separates Strong NP-Completeness Notions
نویسندگان
چکیده
We prove that if for some ǫ > 0, NP contains a set that is DTIME(2n ǫ )-bi-immune, then NP contains a set that is 2-Turing complete for NP (hence 3-truth-table complete) but not 1-truth-table complete for NP. Thus this hypothesis implies a strong separation of completeness notions for NP. Lutz and Mayordomo [LM96] and Ambos-Spies and Bentzien [ASB00] previously obtained the same consequence using strong hypotheses involving resource-bounded measure and/or category theory. Our hypothesis is weaker and involves no assumptions about stochastic properties of NP.
منابع مشابه
Separating Cook Completeness from Karp-Levin Completeness Under a Worst-Case Hardness Hypothesis
We show that there is a language that is Turing complete for NP but not many-one complete for NP, under a worst-case hardness hypothesis. Our hypothesis asserts the existence of a non-deterministic, double-exponential time machine that runs in time O(2 nc ) (for some c > 1) accepting Σ∗ whose accepting computations cannot be computed by bounded-error, probabilistic machines running in time O(2 ...
متن کاملAutoreducibility of NP-Complete Sets
We study the polynomial-time autoreducibility of NP-complete sets and obtain separations under strong hypotheses for NP. Assuming there is a p-generic set in NP, we show the following: • For every k ≥ 2, there is a k-T-complete set for NP that is k-T autoreducible, but is not k-tt autoreducible or (k − 1)-T autoreducible. • For every k ≥ 3, there is a k-tt-complete set for NP that is k-tt autor...
متن کاملar X iv : c s . C C / 0 40 70 15 v 2 2 9 Ju n 20 05 Resource Bounded Immunity and Simplicity ∗
Revisiting the thirty years-old notions of resource-bounded immunity and simplicity, we investigate the structural characteristics of various immunity notions: strong immunity, almost immunity, and hyperimmunity as well as their corresponding simplicity notions. We also study limited immunity and simplicity, called k-immunity and feasible k-immunity, and their simplicity notions. Finally, we pr...
متن کاملResource Bounded Immunity and Simplicity
Revisiting the thirty years-old notions of resource-bounded immunity and simplicity, we investigate the structural characteristics of various immunity notions: strong immunity, almost immunity, and hyperimmunity as well as their corresponding simplicity notions. We also study limited immunity and simplicity, called k-immunity and feasible k-immunity, and their simplicity notions. Finally, we pr...
متن کاملSeparation of NP-Completeness Notions
We use hypotheses of structural complexity theory to separate various NP-completeness notions. In particular, we introduce an hypothesis from which we describe a set in NP that is T-complete but not P tt -complete. We provide fairly thorough analyses of the hypotheses that we introduce.
متن کامل