Time-Space Lower Bounds for Satisfiability

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Time-Space Lower Bounds for Satisfiability (2004)

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by Lance Fortnow , Richard Lipton , Dieter van Melkebeek , Anastasios Viglas

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BibTeX

@MISC{Fortnow04time-spacelower,
    author = {Lance Fortnow and Richard Lipton and Dieter van Melkebeek and Anastasios Viglas},
    title = {Time-Space Lower Bounds for Satisfiability},
    year = {2004}
}

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Abstract

We establish the first polynomial time-space lower bounds for satisfiability on general models of computation. We show that for any constant c less than the golden ratio there exists a positive constant d such that no deterministic random-access Turing machine can solve satisfiability in time n c and space n d, where d approaches 1 when c does. On conondeterministic instead of deterministic machines, we prove the same for any constant c less than √ 2. Our lower bounds apply to nondeterministic linear time and almost all natural NP-complete problems known. In fact, they even apply to the class of languages that can be solved on a nondeterministic machine in linear time and space n 1/c. Our proofs follow the paradigm of indirect diagonalization. We also use that paradigm to prove time-space lower bounds for languages higher up in the polynomial-time hierarchy.

Keyphrases

time-space lower bound polynomial-time hierarchy nondeterministic linear time first polynomial time-space deterministic random-access turing machine linear time natural np-complete problem deterministic machine golden ratio nondeterministic machine indirect diagonalization general model positive constant

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