On the Tape-Number Problem for Deterministic Time Classes

Armin Hemmerling

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arXiv · 1309.7457

On the Tape-Number Problem for Deterministic Time Classes

Armin Hemmerling

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Abstract

For any time bound f, let H(f) denote the hierarchy conjecture which means that the restriction of the numbers of work tapes of deterministic Turing machines to some b generates an infinite hierarchy of proper subclasses DTIME_b(f) \subset \DTIME(f). We show that H(f) implies separations of deterministic from nondeterministic time classes. H(f) follows from the gap property, G(f), which says that there is a time-constructible bound f_2 such that f \in o(f_2) and DTIME(f)=DTIME(f_2). G(f) implies further separations. All these relationships relativize.

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BibTeX RIS

Armin Hemmerling. 2013-09-28. On the Tape-Number Problem for Deterministic Time Classes. https://arxiv.org/abs/1309.7457

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