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Published in:
2008 | OriginalPaper | Chapter
A Well-Mixed Function with Circuit Complexity 5n ±o(n): Tightness of the Lachish-Raz-Type Bounds
Authors : Kazuyuki Amano, Jun Tarui
Published in: Theory and Applications of Models of Computation
Publisher: Springer Berlin Heidelberg
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A Boolean function on
n
variables is called
k
-mixed if for any two different restrictions fixing the same set of
k
variables must induce different functions on the remaining
n
−
k
variables. In this paper, we give an explicit construction of an
n
−
o
(
n
)-mixed Boolean function whose circuit complexity over the basis
U
2
is 5
n
+
o
(
n
). This shows that a lower bound method on the size of a
U
2
-circuit that uses the property of
k
-mixed, which gives the current best lower bound of 5
n
−
o
(
n
) on a
U
2
-circuit size (Iwama, Lachish, Morizumi and Raz [STOC ’01, MFCS ’02]), has reached the limit.