We investigate autoreducibility properties of complete sets for $\cNEXP$ under different polynomial reductions.
Specifically, we show under some polynomial reductions that there is are complete sets for
$\cNEXP$ that are not autoreducible. We obtain the following results:
- There is a $\reduction{p}{tt}$-complete set for $\cNEXP$ that is not $\reduction{p}{btt}$-autoreducible.
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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 >>>