On reductions of NP sets to sparse sets
نویسندگان
چکیده
منابع مشابه
On 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 کاملOn Random Reductions from Sparse Sets to Tally Sets
We s h o w that every sparse set S can be many-one reduced to an appropriate tally set T by a polynomial-time, randomized reduction (see formal deenitions below.) Since T is in NP if S is in NP, this result can be used to show that there is a tally set in NP being randomized many-one complete for all sparse sets in NP. This partially answers an open problem posed by Hartmanis and Yesha 6]. In 6...
متن کاملLearning Reductions to Sparse Sets
We study the consequences of NP having non-uniform polynomial size circuits of various types. We continue the work of Agrawal and Arvind [1] who study the consequences of Sat being many-one reducible to functions computable by non-uniform circuits consisting of a single weighted threshold gate. (Sat ≤m LT1). They claim that P = NP follows as a consequence, but unfortunately their proof was inco...
متن کاملComparing 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 کاملSparse Sets, Approximable Sets, and Parallel Queries to NP
We show that if an NP-complete set or a coNP-complete set is polynomial-time disjunc-tive truth-table reducible to a sparse set then FP NP jj = FP NP log]. With a similar argument we show also that if SAT is O(log n)-approximable then FP NP jj = FP NP log]. Since FP NP jj = FP NP log] implies that SAT is O(logn)-approximable BFT97], it follows from our result that the two hypotheses are equival...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1994
ISSN: 0022-0000
DOI: 10.1016/s0022-0000(05)80006-6