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MFCS
2010
Springer
10 years 2 months ago
Breaking the Rectangle Bound Barrier against Formula Size Lower Bounds
Karchmer, Kushilevitz and Nisan formulated the formula size problem as an integer programming problem called the rectangle bound and introduced a technique called the LP bound, whi...
Kenya Ueno
IPL
2006
88views more  IPL 2006»
10 years 4 months ago
Improved construction for universality of determinant and permanent
Valiant (1979) proved that every polynomial of formula size e is a projection of the (e + 2)
Hong Liu, Kenneth W. Regan
COCO
2005
Springer
150views Algorithms» more  COCO 2005»
10 years 9 months ago
The Quantum Adversary Method and Classical Formula Size Lower Bounds
We introduce two new complexity measures for Boolean functions, which we name sumPI and maxPI. The quantity sumPI has been emerging through a line of research on quantum query com...
Sophie Laplante, Troy Lee, Mario Szegedy
STACS
2007
Springer
10 years 10 months ago
A New Rank Technique for Formula Size Lower Bounds
We exactly determine the formula size of the parity function. If n = 2 + k, where 0 ≤ k < 2 , then the formula size of parity on n bits is 2 (2 + 3k) = n2 + k2 − k2 . Khrap...
Troy Lee
STACS
2009
Springer
10 years 11 months ago
A Stronger LP Bound for Formula Size Lower Bounds via Clique Constraints
We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan [11] and the theory of...
Kenya Ueno
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