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IPL
2006

Monotone circuits for monotone weighted threshold functions

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Monotone circuits for monotone weighted threshold functions
Weighted threshold functions with positive weights are a natural generalization of unweighted threshold functions. These functions are clearly monotone. However, the naive way of computing them is adding the weights of the satisfied variables and checking if the sum is greater than the threshold; this algorithm is inherently non-monotone since addition is a non-monotone function. In this work we by-pass this addition step and construct a polynomial size logarithmic depth unbounded fan-in monotone circuit for every weighted threshold function, i.e., we show that weighted threshold functions are in mAC1 . (To the best of our knowledge, prior to our work no polynomial monotone circuits were known for weighted threshold functions.) Our monotone circuits are applicable for the cryptographic tool of secret sharing schemes. Using general results for compiling monotone circuits (Yao, 1989) and monotone formulae (Benaloh and Leichter, 1990) into secret sharing schemes, we get secret sharing sc...
Amos Beimel, Enav Weinreb
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2006
Where IPL
Authors Amos Beimel, Enav Weinreb
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