Martin Sauerhoff

In this paper, we are concerned with randomized OBDDs and randomized

read-k-times branching programs. We present an example of a Boolean

function which has polynomial size randomized OBDDs with small,

one-sided error, but only non-deterministic read-once branching

programs of exponential size. Furthermore, we discuss a lower bound

technique for randomized ...
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Jayram S. Thathachar

We obtain an exponential separation between consecutive

levels in the hierarchy of classes of functions computable by

polynomial-size syntactic read-$k$-times branching programs, for

{\em all\/} $k>0$, as conjectured by various

authors~\cite{weg87,ss93,pon95b}. For every $k$, we exhibit two

explicit functions that can be computed by linear-sized

read-$(\kpluso)$-times branching programs but ...
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Martin Sauerhoff

We extend the tools for proving lower bounds for randomized branching

programs by presenting a new technique for the read-once case which is

applicable to a large class of functions. This technique fills the gap

between simple methods only applicable for OBDDs and the well-known

"rectangle technique" of Borodin, Razborov ...
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Li Chen, Bin Fu

It is well known that every finite Abelian group $G$ can be

represented as a product of cyclic groups: $G=G_1\times

G_2\times\cdots G_t$, where each $G_i$ is a cyclic group of size

$p^j$ for some prime $p$ and integer $j\ge 1$. If $a_i$ is the

generator of the cyclic group of ...
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Emanuele Viola

We show that the promise problem of distinguishing $n$-bit strings of hamming weight $\ge 1/2 + \Omega(1/\log^{d-1} n)$ from strings of weight $\le 1/2 - \Omega(1/\log^{d-1} n)$ can be solved by explicit, randomized (unbounded-fan-in) poly(n)-size depth-$d$ circuits with error $\le 1/3$, but cannot be solved by deterministic poly(n)-size depth-$(d+1)$ circuits, ... more >>>