We show the following results regarding complete sets:

NP-complete sets and PSPACE-complete sets are many-one
autoreducible.

Complete sets of any level of PH, MODPH, or
the Boolean hierarchy over NP are many-one autoreducible.

EXP-complete sets are many-one mitotic.

NEXP-complete sets are weakly many-one mitotic.

PSPACE-complete sets are weakly Turing-mitotic.

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<p> We study the question of the existence of non-mitotic sets in NP. We show under various hypotheses that:</p>
<ul>
<li>1-tt-mitoticity and m-mitoticity differ on NP.</li>
<li>1-tt-reducibility and m-reducibility differ on NP.</li>
<li>There exist non-T-autoreducible sets in NP (by a result from Ambos-Spies, these sets are neither ... more >>>

We investigate the autoreducibility and mitoticity of complete sets for several classes with respect to different polynomial-time and logarithmic-space reducibility notions.

Previous work in this area focused on polynomial-time reducibility notions. Here we obtain new mitoticity and autoreducibility results for the classes EXP and NEXP with respect to some restricted ... more >>>

We study the autoreducibility and mitoticity of complete sets for NP and other complexity classes, where the main focus is on logspace reducibilities. In particular, we obtain:
- For NP and all other classes of the PH: each logspace many-one-complete set is logspace Turing-autoreducible.
- For P, the delta-levels of ... more >>>