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 -