Abstract
In this paper we consider the problem of computing threshold functions using directed monotone contact networks. We give constructions of monotone contact networks of size ( k-1)( n- k+2)⌈ log( n- k+2)⌉ computing T n k , for2 ⩽ k⩽ n-1. Our upper bound is close to the ω( kn log( n/ k-1))) lower bound for small thresholds and the k( n- k+1) lower bound for large thresholds. Our networks are described explicitly; we do not use probabilistic existence arguments.
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