Multilinearity Can Be Exponentially Restrictive (preliminary Version)

  title={Multilinearity Can Be Exponentially Restrictive (preliminary Version)},
  author={Rimli Sengupta},
We deene a Boolean circuit to be multilinear if the formal polynomial associated with it is multilinear as well. We consider the problem of computing the connectiv-ity 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(n 3), our lower bound establishes that at least in the context of monotone computation, mul… CONTINUE READING

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