Christian Glaßer, Stephen Travers, Klaus W. Wagner

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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Valentine Kabanets, Osamu Watanabe

The Valiant-Vazirani Isolation Lemma [TCS, vol. 47, pp. 85--93, 1986] provides an efficient procedure for isolating a satisfying assignment of a given satisfiable circuit: given a Boolean circuit $C$ on $n$ input variables, the procedure outputs a new circuit $C'$ on the same $n$ input variables with the property that ... more >>>

Shuichi Hirahara

We exactly characterize the average-case complexity of the polynomial-time hierarchy (PH) by the worst-case (meta-)complexity of GapMINKT(PH), i.e., an approximation version of the problem of determining if a given string can be compressed to a short PH-oracle efficient program. Specifically, we establish the following equivalence:

DistPH is contained in ... more >>>