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TimeSpace Tradeoffs for Satisfiability
 Journal of Computer and System Sciences
, 1997
"... We give the first nontrivial modelindependent timespace 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 randomaccess nondeterministic Turing machines. In particular, SAT cannot be solved ..."
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Cited by 29 (1 self)
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We give the first nontrivial modelindependent timespace 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 randomaccess 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 logspace 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 polynomialtime 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...
On the Complexity of SAT
, 1999
"... We show that nondeterministic time NT IME(n) is not contained in deterministic time n # 2# and polylogarithmic space, for any # > 0. This implies that (infinitely often) satisfiability cannot be solved in time O(n # 2# ) and polylogarithmic space. A similar result is presented for uniform circui ..."
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Cited by 24 (1 self)
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We show that nondeterministic time NT IME(n) is not contained in deterministic time n # 2# and polylogarithmic space, for any # > 0. This implies that (infinitely often) satisfiability cannot be solved in time O(n # 2# ) and polylogarithmic space. A similar result is presented for uniform circuits.
A Theory Of Strict PCompleteness
 STACS 1992, in Lecture Notes in Computer Science 577
, 1992
"... . A serious limitation of the theory of Pcompleteness is that it fails to distinguish between those Pcomplete problems that do have polynomial speedup on parallel machines from those that don't. We introduce the notion of strict Pcompleteness and develop tools to prove precise limits on the possi ..."
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Cited by 10 (0 self)
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. A serious limitation of the theory of Pcompleteness is that it fails to distinguish between those Pcomplete problems that do have polynomial speedup on parallel machines from those that don't. We introduce the notion of strict Pcompleteness and develop tools to prove precise limits on the possible speedups obtainable for a number of Pcomplete problems. Key words. Parallel computation; Pcompleteness. Subject classifications. 68Q15, 68Q22. 1. Introduction A major goal of the theory of parallel computation is to understand how much speedup is obtainable in solving a problem on parallel machines over sequential machines. The theory of Pcompleteness has successfully classified many problems as unlikely to have polylog time algorithms on a parallel machine with a polynomial number of processors. However, the theory fails to distinguish between those Pcomplete problems that do have significant, polynomial speedup on parallel machines from those that don't. Yet this distinction is e...