Title:
Multilinearity Can Be Exponentially Restrictive (Preliminary Version)
Multilinearity Can Be Exponentially Restrictive (Preliminary Version)
Authors
Sengupta, Rimli
Venkateswaran, H.
Venkateswaran, H.
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Abstract
We define a Boolean circuit to be multilinear if the formal polynomial
associated with it is multilinear as well. We consider the problem of
computing the connectivity function using circuits that are monotone and
multilinear. Our main result is that monotone multilinear circuits for this
function require exponential size. Since connectivity can be computed by
monotone Boolean circuits within size O(n³), our lower bound establishes that
at least in the context of monotone computation, multilinearity can be
exponentially restrictive. As an application of our lower bound, we show that
connectivity is not in mNL, thereby improving a recent result by Yao
that connectivity is not in mNC¹.
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Date Issued
1994
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176389 bytes
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Text
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Technical Report