MPI-I-92-120
Separating the communication complexities of MOD m and MOD p circuits
Grolmusz, Vince
March 1992, 16 pages.
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Status: available - back from printing
We prove in this paper that it is much harder to evaluate depth--2,
size--$N$ circuits with MOD $m$ gates than with MOD $p$ gates by
$k$--party communication protocols: we show a $k$--party protocol
which communicates $O(1)$ bits to evaluate circuits with MOD $p$ gates,
while evaluating circuits with MOD $m$ gates needs $\Omega(N)$ bits,
where $p$ denotes a prime, and $m$ a composite, non-prime power number.
Let us note that using $k$--party protocols with $k\geq p$ is crucial
here, since there are depth--2, size--$N$ circuits with MOD $p$ gates
with $p>k$, whose $k$--party evaluation needs $\Omega(N)$ bits. As a
corollary, for all $m$, we show a function, computable with a depth--2
circuit with MOD $m$ gates, but not with any depth--2 circuit with MOD
$p$ gates.
It is easy to see that the $k$--party protocols are not weaker than the
$k'$--party protocols, for $k'>k$. Our results imply that if there is a
prime $p$ between $k$ and $k'$: $k
URL to this document: https://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1992-120
BibTeX
@TECHREPORT{Grolmusz92b,
AUTHOR = {Grolmusz, Vince},
TITLE = {Separating the communication complexities of MOD m and MOD p circuits},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
NUMBER = {MPI-I-92-120},
MONTH = {March},
YEAR = {1992},
ISSN = {0946-011X},
}