TY - JOUR
T1 - On the number of ANDs versus the number of ORs in monotone Boolean circuits
AU - Zwick, Uri
PY - 1996/7/8
Y1 - 1996/7/8
N2 - Alon and Boppana showed that if a monotone Boolean function f of n variables can be computed by a monotone circuit containing k AND gates, where k > 1, then it can also be computed using a monotone circuit containing k AND gates and O(k(n + k)) OR gates. They note that their result is tight up to a logarithmic factor. Here we show that under the same assumption the function f can be computed using a monotone circuit containing k AND gates and O(k(n + k)/ log k) OR gates. This result is tight up to a constant factor. By duality the same result holds when the roles of the AND and OR gates are interchanged.
AB - Alon and Boppana showed that if a monotone Boolean function f of n variables can be computed by a monotone circuit containing k AND gates, where k > 1, then it can also be computed using a monotone circuit containing k AND gates and O(k(n + k)) OR gates. They note that their result is tight up to a logarithmic factor. Here we show that under the same assumption the function f can be computed using a monotone circuit containing k AND gates and O(k(n + k)/ log k) OR gates. This result is tight up to a constant factor. By duality the same result holds when the roles of the AND and OR gates are interchanged.
KW - AND and OR gates
KW - Boolean complexity
KW - Circuit complexity
KW - Computational complexity
KW - Monotone complexity
UR - http://www.scopus.com/inward/record.url?scp=30244535270&partnerID=8YFLogxK
U2 - 10.1016/0020-0190(96)00080-4
DO - 10.1016/0020-0190(96)00080-4
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AN - SCOPUS:30244535270
SN - 0020-0190
VL - 59
SP - 29
EP - 30
JO - Information Processing Letters
JF - Information Processing Letters
IS - 1
ER -