We prove that if for some epsilon > 0 NP contains a set that is
DTIME(2^{n^{epsilon}})-bi-immune, then NP contains a set that 2-Turing
complete for NP but not 1-truth-table complete for NP. Lutz and Mayordomo
(LM96) and Ambos-Spies and Bentzien (AB00) previously obtained the
same consequence using strong ... more >>>

A language is called k-membership comparable if there exists a
polynomial-time algorithm that excludes for any k words one of
the 2^k possibilities for their characteristic string.
It is known that all membership comparable languages can be
reduced to some P-selective language with polynomially many
adaptive queries. We show however ... more >>>

We present the first example of a natural distribution on instances
of an NP-complete problem, with the following properties.
With high probability a random formula from this
distribution (a) is unsatisfiable,
(b) has a short proof that can be found easily, and (c) does not have a short
(general) resolution ... more >>>