The complexity of Boolean functions
The complexity of Boolean functions
Entropy of contact circuits and lower bounds on their complexity
Theoretical Computer Science - International Symposium on Mathematical Foundations of Computer Science, Bratisl
Explicit lower bound of 4.5n - o(n) for boolena circuits
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
An Explicit Lower Bound of 5n - o(n) for Boolean Circuits
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Small Pseudo-Random Sets Yield Hard Functions: New Tight Explict Lower Bounds for Branching Programs
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Asymptotically Optimal Circuit for a Storage Access Function
IEEE Transactions on Computers
Counting Responders in an Associative Memory
IEEE Transactions on Computers
| Hi-index | 5.23 |
A Boolean function on n variables is k-mixed if any two distinct restrictions fixing the same set of k variables induce distinct functions on the remaining n-k variables. We give an explicit construction of an (n-o(n))-mixed Boolean function whose circuit complexity over the basis U"2 is 5n+o(n). This shows that a lower bound method for the size of a U"2-circuit that applies to arbitrary well-mixed functions, which yields the largest known lower bound of 5n-o(n) for the U"2-circuit size (Iwama, Lachish, Morizumi and Raz [STOC01, MFCS02]), has reached the limit.