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...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1994
ISSN: 0022-0000
DOI: 10.1016/s0022-0000(05)80006-6