Two time-space tradeoffs for element distinctness

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Abstract

Two time-space tradeoffs for element distinctness are given. The first one shows T2S = Ω(n3) on a branching program using minimum operations. By a result of Yao (1982), this implies the same bounds for linear queries. The second result extends one by Duris and Galil (1984) who constructed a Boolean function that requires T2S = Ω(n3) on a k-headed Turing machine. Here it is shown that their proof also holds for element distinctness, a more natural problem.

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