The complexity of Boolean functions
The complexity of Boolean functions
Improvements on Khrapchenko's theorem
Theoretical Computer Science
On submodular complexity measures
Poceedings of the London Mathematical Society symposium on Boolean function complexity
Fractional Covers and Communication Complexity
SIAM Journal on Discrete Mathematics
The Shrinkage Exponent of de Morgan Formulas is 2
SIAM Journal on Computing
On notions of information transfer in VLSI circuits
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
THE QUANTUM ADVERSARY METHOD AND CLASSICAL FORMULA SIZE LOWER BOUNDS
Computational Complexity
Negative weights make adversaries stronger
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Lower bounds in communication complexity based on factorization norms
Random Structures & Algorithms
A new rank technique for formula size lower bounds
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Breaking the rectangle bound barrier against formula size lower bounds
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
On the nonnegative rank of distance matrices
Information Processing Letters
| Hi-index | 5.23 |
Khrapchenko's classical lower bound n^2 on the formula size of the parity function f can be interpreted as designing a suitable measure of sub-rectangles of the combinatorial rectangle f^-^1(0)xf^-^1(1). Trying to generalize this approach we arrived at the concept of convex measures. We prove the negative result that convex measures are bounded by O(n^2) and show that several measures considered for proving lower bounds on the formula size are convex. We also prove quadratic upper bounds on a class of measures that are not necessarily convex.