How Do Read-Once Formulae Shrink?

Moshe Dubiner, Uri Zwick

Research output: Contribution to journalArticlepeer-review

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 [formula omitted]. This result is asymptotically the tightest possible. It improves a similar result obtained recently by Håstad, Razborov and Yao.

Original languageEnglish
Pages (from-to)455-469
Number of pages15
JournalCombinatorics Probability and Computing
Volume3
Issue number4
DOIs
StatePublished - Dec 1994

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