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by David A. Mix Barrington, Richard Beigel, Steven Rudich
Computational Complexity
http://1013seopc.eecs.uic.edu/papers/bbr-mods-cc.PS.gz
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Abstract:
Abstract. Define the MODm-degree of a boolean function F to be the smallest degree of any polynomial P, over the ring of integers modulo m, such that for all 0-1 assignments ~x, F (~x) = 0 iff P (~x) = 0. We obtain the unexpected result that the MODm-degree of the OR of N variables is O( r p N), where r is the number of distinct prime factors of m. This is optimal in the case of representation by symmetric polynomials. The MOD n function is 0 if the number of input ones is a multiple of n and is one otherwise. We show that the MODm-degree of both the MOD n and:MOD n functions is
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