Non-mitotic sets

Document Type

Article

Publication Date

5-17-2009

Abstract

We study the question of the existence of non-mitotic sets in NP. We show under various hypotheses that

  • 1-tt-mitoticity and m-mitoticity differ on NP.

  • T-autoreducibility and T-mitoticity differ on NP (this contrasts the situation in the recursion theoretic setting, where Ladner showed that autoreducibility and mitoticity coincide).

  • 2-tt-autoreducibility does not imply weak 2-tt-mitoticity (from this it follows that autoreducibility and mitoticity are not equivalent for all reducibilities between 2-tt and T, although the notions coincide for m- and 1-tt-reducibility).

Comments

Under an Elsevier user license

Publication Title

Theoretical Computer Science

DOI

10.1016/j.tcs.2008.12.043

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