Technical Report CS0679

Authors: E. Aharonson and H. Attiya
PDF - RevisedCS0679.revised.pdf
PDF - Revised againCS0679.revised2.pdf
Abstract: It is shown that an acyclic smooting network (and hence counting network) of fan-out $n$ cannot be constructed from balancers of fan-out $b_{1},...,b_{k}$, if there exists a prime factor $p$ of $n$, such that $p$ does not divide $b_{i}$, for all $i, 1 \leq i \leq k$. This holds regardless of the depth of the network, as long as it is finite. In particular, only smoothing networks of fan-out $2^{\ell}$ (for a non-negative integer $\ell$ ) can be constructed out of 2-balancers. A very simple construction of {\em cyclic} counting networks with fan-out $n$ is presented. Proving the correctness of this construction involves a novel technique of arguing about counting networks in non-quiescent states.
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