Computer Science > Computational Complexity
[Submitted on 2 Mar 2020 (v1), last revised 13 Jul 2020 (this version, v2)]
Title:Hardness of Sparse Sets and Minimal Circuit Size Problem
View PDFAbstract: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 $2^{n^{o(1)}}$-sparse set in $NTIME(2^{n^{o(1)}})$ that does not have any randomized streaming algorithm with $n^{o(1)}$ updating time, and $n^{o(1)}$ space, then $NEXP\not=BPP$, 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 $EXP\not=ZPP$.
Submission history
From: Bin Fu [view email][v1] Mon, 2 Mar 2020 05:20:27 UTC (21 KB)
[v2] Mon, 13 Jul 2020 00:24:05 UTC (22 KB)
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