Time-Space Tradeoffs for Satisfiability

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Time-Space Tradeoffs for Satisfiability (1997)

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by Lance Fortnow

Venue:	Journal of Computer and System Sciences
Citations:	37 - 1 self

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@ARTICLE{Fortnow97time-spacetradeoffs,
    author = {Lance Fortnow},
    title = {Time-Space Tradeoffs for Satisfiability},
    journal = {Journal of Computer and System Sciences},
    year = {1997},
    volume = {60},
    pages = {2000}
}

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Abstract

We give the first nontrivial model-independent time-space tradeoffs for satisfiability. Namely, we show that SAT cannot be solved simultaneously in n 1+o(1) time and n 1\Gammaffl space for any ffl ? 0 on general random-access nondeterministic Turing machines. In particular, SAT cannot be solved deterministically by a Turing machine using quasilinear time and p n space. We also give lower bounds for log-space uniform NC 1 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 a...

Keyphrases

time-space tradeoff sat cannot log-space uniform nc polynomial-time hierarchy nonconstant number quasilinear time nondeterministic computation proof us simple diagonalization yield first nontrivial model-independent time-space tradeoff gammaffl space sublinear space general random-access nondeterministic turing machine super linear time small amount main result turing machine basic idea new approach linear time

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