Time–Space Tradeoffs for SAT on Nonuniform Machines

Iannis Tourlakis
2001 Journal of computer and system sciences (Print)  
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 e > 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 − e ) advice nor by a random access deterministic Turing machine using n 1+o(1) time, n 1 − e space, and n 1 − e
more » ... e. More generally, we show that if for some e > 0 there exists a random access deterministic Turing machine solving SAT using n a time, n b space, and o(n (a+b)/2 − e ) advice, then a \ 1 2 ('b 2 +8 − b). Lower bounds for computing 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 e > 0 and all rational numbers r \ 1, DTISP(n r , n 1 − e ) is properly contained in NTIME(n r ).
doi:10.1006/jcss.2001.1767 fatcat:lmusmuoedfhtdetal3y7gejopm