TY - JOUR

T1 - How Do Read-Once Formulae Shrink?

AU - Dubiner, Moshe

AU - Zwick, Uri

PY - 1994/12

Y1 - 1994/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84974189031&partnerID=8YFLogxK

U2 - 10.1017/S0963548300001358

DO - 10.1017/S0963548300001358

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AN - SCOPUS:84974189031

SN - 0963-5483

VL - 3

SP - 455

EP - 469

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

IS - 4

ER -