Approximating the Number of Solutions of a {\ G F [ 2 ]} Polynomial

Authors:
Marek Karpinski;Michael Luby
Affiliations:
-;-
Venue:
Approximating the Number of Solutions of a {\' G F [ 2 ]} Polynomial
Year:
1990

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Fast range-summable random variables for efficient aggregate estimation

Proceedings of the 2006 ACM SIGMOD international conference on Management of data

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Abstract

We develop a polynomial time Monte-Carlo algorithm for estimating the number of solutions to a multivariate polynomial over $GF(2)$. This gives the first efficient method for estimating the number of points on algebraic varieties over $GF(2)$, the problem recently proven to be $\#P$-\complete\/ even for the cubic polynomials. The number of applications of the result has been also discussed.