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Electronic Colloquium on Computational Complexity

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Reports tagged with immunity:
TR04-019 | 15th January 2004
Christian Glaßer, A. Pavan, Alan L. Selman, Samik Sengupta

Properties of NP-Complete Sets

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 ... more >>>

TR05-011 | 21st December 2004
Christian Glaßer, Mitsunori Ogihara, A. Pavan, Alan L. Selman, Liyu Zhang

Autoreducibility, Mitoticity, and Immunity

We show the following results regarding complete sets:

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

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 >>>

TR08-027 | 4th December 2007
Till Tantau

Generalizations of the Hartmanis-Immerman-Sewelson Theorem and Applications to Infinite Subsets of P-Selective Sets

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 >>>

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