论文信息 - Bounds for the Element Distinctness Problem on one-tape Turing machines

Bounds for the Element Distinctness Problem on one-tape Turing machines

We disprove a conjecture of Lopez-Ortiz by showing that the Element Distinctness Problem for n numbers of size O(logn) can be solved in O(n2(logn)3/2(loglogn)1/2) steps by a nondeterministic one-tape Turing machine. Further we give a simplified algorithm for solving the problem for shorter numbers in time O(n2 log n) on a deterministic one-tape Turing machine and a new proof of the matching lower bound.

Holger Petersen

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