Non-mitotic Sets

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. -- 1-tt-complete sets for NP are nonuniformly m-complete.

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