We analyze the efficiency of the random walk algorithm on random 3CNF instances, and prove em linear upper bounds on the running time
of this algorithm for small clause density, less than 1.63. Our upper bound matches the observed running time to within a multiplicative factor. This is the ... more >>>

A recursive enumerator for a function $h$ is an algorithm $f$ which
enumerates for an input $x$ finitely many elements including $h(x)$.
$f$ is an $k(n)$-enumerator if for every input $x$ of length $n$, $h(x)$
is among the first $k(n)$ elements enumerated by $f$.
If there is a $k(n)$-enumerator for ... more >>>

Variants of Kannan's Theorem are given where the circuits of
the original theorem are replaced by arbitrary recursively presentable
classes of languages that use advice strings and satisfy certain mild
conditions. These variants imply that $\DTIME(n^{k'})^{\NE}/n^k$
does not contain $\PTIME^{\NE}$, $\DTIME(2^{n^{k'}})/n^k$ does
not contain $\EXP$, $\SPACE(n^{k'})/n^k$ does not ... more >>>