In this article we consider a basic problem in the layout of
VLSI-circuits, the channel-routing problem in the knock-knee mode.
We show that knock-knee channel routing with 3-terminal nets is
NP-complete and thereby settling a problem that was open for more
than a decade. In 1987, Sarrafzadeh showed that knock-knee ... more >>>

We show that every resolution proof of the {\em functional} version
$FPHP^m_n$ of the pigeonhole principle (in which one pigeon may not split
between several holes) must have size $\exp\of{\Omega\of{\frac n{(\log
m)^2}}}$. This implies an $\exp\of{\Omega(n^{1/3})}$ bound when the number
of pigeons $m$ is arbitrary.

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We prove exponential separations between the sizes of
particular refutations in negative, respectively linear, resolution and
general resolution. Only a superpolynomial separation between negative
and general resolution was previously known. Our examples show that there
is no strong relationship between the size and width of refutations in
negative and ... more >>>