117 research outputs found
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(2^2^n^c) (for some c > 1) accepting Sigma^* whose accepting computations cannot be computed by bounded-error, probabilistic machines running in time O(2^2^{beta * 2^n^c) (for some beta > 0). This is the first result that separates completeness notions for NP under a worst-case hardness hypothesis
Hardness of Sparse Sets and Minimal Circuit Size Problem
We develop a polynomial method on finite fields to amplify the hardness of
spare sets in nondeterministic time complexity classes on a randomized
streaming model. One of our results shows that if there exists a
-sparse set in that does not have any
randomized streaming algorithm with updating time, and
space, then , where a -sparse set is a language that has at
most strings of length . We also show that if MCSP is -hard
under polynomial time truth-table reductions, then
Hardness of Sparse Sets and Minimal Circuit Size Problem
We study the magnification of hardness of sparse sets in nondeterministic time complexity classes on a randomized streaming model. One of our results shows that if there exists a 2no(1) -sparse set in NDTIME(2no(1)) that does not have any randomized streaming algorithm with no(1) updating time, and no(1) space, then NEXP≠BPP , where a f(n)-sparse set is a language that has at most f(n) strings of length n. We also show that if MCSP is ZPP -hard under polynomial time truth-table reductions, then EXP≠ZPP
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