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