A binary sequence A=A(0)A(1).... is called i.o. Turing-autoreducible if A is reducible to itself via an oracle Turing machine that never queries its oracle at the current input, outputs either A(x) or a don't-know symbol on any given input x, and outputs A(x) for infinitely many x. If in addition ... more >>>
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.
If ... more >>>
<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 ...
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