Abstract
Let f be a de Morgan read-once function of n variables. Let fε be the random restriction obtained by independently assigning to each variable of f, the value 0 with probability (1 -ε)/2, the value 1 with the same probability, and leaving it unassigned with probability ε. We show that fε depends, on the average, on only O(εαn + εn1/α) variables, where . This result is asymptotically the tightest possible. It improves a similar result obtained recently by Håstad, Razborov and Yao.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Reference20 articles.
1. [9] Håstad J. , Razborov A. and Yao A. (submitted) On the Shrinkage Exponent for Read-Once Formulae.
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