The Expressive Power of Voting Polynomials

  title={The Expressive Power of Voting Polynomials},
  author={James Aspnes and Richard Beigel and Merrick L. Furst and Steven Rudich},
We consider the problem of approximating a Boolean function ~ : {O, 1 }m ~ {O, 1} by an integer polynomial p of degree k. For us, a polynomial p(z) predicts the value of ~(z) if, whenever p(z) ~ O, ~(x) = 1, and whenever p(x) < 0, ~(o) = O. A low-degree polynomial p is a good approximator for .f if it predicts ~ at almost all points. Given a positive integer k, and a Boolean function j, we ask, “how good is the best degree k approximation to j?” We introduce a new lower bound technique which… CONTINUE READING


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26th Annual Symposium on Foundations of Computer Science (sfcs 1985) • 1985
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