We prove that the Cutting Plane proof system based on
Gomory-Chvatal cuts polynomially simulates the
lift-and-project system with integer coefficients
written in unary. The restriction on coefficients can be
omitted when using Krajicek's cut-free Gentzen-style extension
of both systems. We also prove that Tseitin tautologies
have short proofs in ... more >>>

We study the question of whether the class DisNP of
disjoint pairs (A, B) of NP-sets contains a complete pair.
The question relates to the question of whether optimal
proof systems exist, and we relate it to the previously
studied question of whether there exists ... more >>>

The satisfiability problem of Boolean Formulae in 3-CNF (3-SAT)
is a well known NP-complete problem and the development of faster
(moderately exponential time) algorithms has received much interest
in recent years. We show that the 3-SAT problem can be solved by a
probabilistic algorithm in expected time O(1,3290^n).
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