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 -