Given a set of monomials, the Minimum AND-Circuit problem asks for a
circuit that computes these monomials using AND-gates of fan-in two and
being of minimum size. We prove that the problem is not polynomial time
approximable within a factor of less than 1.0051 unless P = NP, even if
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We present a deterministic algorithm producing the number of
$k$-colourings of a graph on $n$ vertices in time
$2^nn^{O(1)}$.
We also show that the chromatic number can be found by a
polynomial space algorithm running in time $O(2.2461^n)$.
Finally, we present a family of ... more >>>

Let $\phi$ be a 3CNF formula with n variables and m clauses. A
simple nonconstructive argument shows that when m is
sufficiently large compared to n, most 3CNF formulas are not
satisfiable. It is an open question whether there is an efficient
refutation algorithm that for most such formulas proves ... more >>>