Christian Glaßer, A. Pavan, Alan L. Selman, Samik Sengupta

We study several properties of sets that are complete for NP.

We prove that if $L$ is an NP-complete set and $S \not\supseteq L$ is a p-selective sparse set, then $L - S$ is many-one-hard for NP. We demonstrate existence of a sparse set $S \in \mathrm{DTIME}(2^{2^{n}})$

such ...
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Christian Glaßer, Mitsunori Ogihara, A. Pavan, Alan L. Selman, Liyu Zhang

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.

... more >>>Till Tantau

The Hartmanis--Immerman--Sewelson theorem is the classical link between the exponential and the polynomial time realm. It states that NE = E if, and only if, every sparse set in NP lies in P. We establish similar links for classes other than sparse sets:

1. E = UE if, and only ... more >>>