منابع مشابه
Comparing Reductions to NP-Complete Sets
Under the assumption that NP does not have p-measure 0, we investigate reductions to NP-complete sets and prove the following: 1. Adaptive reductions are more powerful than nonadaptive reductions: there is a problem that is Turing-complete for NP but not truth-table-complete. 2. Strong nondeterministic reductions are more powerful than deterministic reductions: there is a problem that is SNP-co...
متن کاملOn Reductions of NP Sets to Sparse Sets
We prove unlikely consequences of the existence of sparse hard sets for P under deterministic as well as one-sided error randomized truth-table reductions. Our main results are as follows. We establish that the existence of a polynomially dense hard set for P under (randomized) logspace bounded truth-table reductions implies that P (R)L, and that the collapse goes down to P (R)NC 1 in case of r...
متن کاملSplitting NP-Complete Sets
We show that a set is m-autoreducible if and only if it is m-mitotic. This solves a long standing open question in a surprising way. As a consequence of this unconditional result and recent work by Glaßer et al., complete sets for all of the following complexity classes are m-mitotic: NP, coNP, ⊕P, PSPACE, and NEXP, as well as all levels of PH, MODPH, and the Boolean hierarchy over NP. In the c...
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 کاملStrong Reductions and Isomorphism of Complete Sets
We study the structure of the polynomial-time complete sets for NP and PSPACE under strong nondeterministic polynomial-time reductions (SNP-reductions). We show the following results. • If NP contains a p-random language, then all polynomial-time complete sets for PSPACE are SNP-isomorphic. • If NP ∩ co-NP contains a p-random language, then all polynomial-time complete sets for NP are SNP-isomo...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 2007
ISSN: 0890-5401
DOI: 10.1016/j.ic.2006.10.005