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• W2006558104 abstract "The arguments used by R. Kannan (1984, Math. Systems Theory 17 , 29–45), L. Fortnow (1997, in “Proceedings, Twelfth Annual IEEE Conference on Computational Complexity, Ulm, Germany, 24–27 June, 1997,” pp. 52–60), and R. J. Lipton and A. Viglas (1999, in “40th Annual Symposium on Foundations of Computer Science, New York, 17–19 Oct. 1999,” pp. 459–469) are generalized and combined with an argument for diagonalizing over machines taking n bits of advice on inputs of length n to obtain the first nontrivial time–space lower bounds for SAT on nonuniform machines. In particular, we show that for any a < 2 and any ε >0, SAT cannot be computed by a random access deterministic Turing machine using n a time, n o (1) space, and o ( n 2 /2− ε ) advice nor by a random access deterministic Turing machine using n 1+ o (1) time, n 1− ε space, and n 1− ε advice. More generally, we show that if for some ε >0 there exists a random access deterministic Turing machine solving SAT using n a time, n b space, and o ( n ( a + b )/2− ε ) advice, then a ⩾ 1 2 ( b 2 +8 − b ). Lower bounds for computing overline {{ bf SAT }} on random access nondeterministic Turing machines taking sublinear advice are also obtained. Moreover, we show that SAT does not have NC 1 circuits of size n l + o (1) generated by a nondeterministic log–space machine taking n o (1) advice. Additionally, new separations of uniform classes are obtained. We show that for all ε >0 and all rational numbers r ⩾1, DTISP( n r , n 1− ε ) is properly contained in NTIME( n r )." @default.
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• W2006558104 date "2001-09-01" @default.
• W2006558104 modified "2023-09-29" @default.
• W2006558104 title "Time–Space Tradeoffs for SAT on Nonuniform Machines" @default.
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• W2006558104 doi "https://doi.org/10.1006/jcss.2001.1767" @default.
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