Time-Space Tradeoffs for Nondeterministic Computation

We show new tradeoffs for satisfiability and nondeterministic linear time. Satisfiability cannot be solved on general purpose random-access Turing machines in time n and space n. This improves recent results of Fortnow and of Lipton and Viglas. In general, for any constant a less than the golden ratio, we prove that satisfiability cannot be solved in time n and space n for some positive constant b. Our techniques allow us to establish this result for b < 12( a+2 a2 − a). We can do better for a close to the golden ratio, for example, satisfiability cannot be solved by a random-access Turing machine using n time and n space. We also show the first nontrivial lower bounds for nondeterministic linear time machines using sublinear space. For example, there exists a language computable in nondeterministic linear time and n space that cannot be computed in deterministic n time and n space. Higher up the polynomial-time hierarchy we can get better bounds. We show that lineartime Σ`-computations require essentially n ` time if we only allow n space. We also show new lower bounds on conondeterministic versus nondeterministic computation. Electronic Colloquium on Computational Complexity, Report No. 28 (2000)