We introduce the polynomial-time tree reducibility
(ptt-reducibility). Our main result states that for
languages $B$ and $C$ it holds that
$B$ ptt-reduces to $C$ if and only if
the unbalanced leaf-language class of $B$ is robustly contained in
the unbalanced leaf-language class of $C$.
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Khot formulated in 2002 the "Unique Games Conjectures" stating that, for any epsilon > 0, given a system of constraints of a certain form, and the promise that there is an assignment that satisfies a 1-epsilon fraction of constraints, it is intractable to find a solution that satisfies even an ... more >>>

An algorithm is presented for counting the number of maximum weight satisfying assignments of a 2SAT formula. The worst case running time of $O(\mbox{poly($n$)} \cdot 1.2461^n)$ for formulas with $n$ variables improves on the previous bound of $O(\mbox{poly($n$)} \cdot 1.2561^n)$ by Dahll\"of, Jonsson, and Wahlstr\"om . The weighted 2SAT counting ... more >>>