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JCSS
2000

Time-Space Tradeoffs for Satisfiability

13 years 3 months ago
Time-Space Tradeoffs for Satisfiability
We give the first nontrivial model-independent time-space tradeoffs for satisfiability. Namely, we show that SAT cannot be solved simultaneously in n1+o(1) time and n1space for any > 0 on general random-access nondeterministic Turing machines. In particular, SAT cannot be solved deterministically by a Turing machine using quasilinear time and n space. We also give lower bounds for log-space uniform NC1 circuits and branching programs. Our proof uses two basic ideas. First we show that if SAT can be solved nondeterministically with a small amount of time then we can collapse a nonconstant number of levels of the polynomial-time hierarchy. We combine this work with a result of Nepomnjascii that shows that a nondeterministic computation of super linear time and sublinear space can be simulated in alternating linear time. A simple diagonalization yields our main result. We discuss how these bounds lead to a new approach to separating the complexity classes NL and NP. We give some poss...
Lance Fortnow
Added 18 Dec 2010
Updated 18 Dec 2010
Type Journal
Year 2000
Where JCSS
Authors Lance Fortnow
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