On the number of ANDs versus the number of ORs in monotone Boolean circuits
Download:
|
|
by Uri Zwick
http://www.cs.tau.ac.il/%7Ezwick/papers/and-or.ps.gz
Add To MetaCart
Abstract:
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.
Citations
| 2004 | The Design and Analysis of Computer Algorithms – Aho, Hopcroft, et al. - 1974 |
| 304 | The complexity of Boolean functions – Wegener - 1987 |
| 114 | The monotone circuit complexity of boolean functions – Alon, Boppana - 1987 |
| 40 | On Economical Construction of the Transitive Closure of a Directed Graph – Arlazarov, Dinic, et al. - 1970 |
| 40 | The Complexity of Boolean Networks – Dunne - 1988 |
| 9 | An algorithm for the computation of linear forms – Savage - 1974 |
| 2 | The complexity of monotone boolean functions and an algorithm for finding shortest paths in a graph – Bloniarz - 1979 |
| 1 | O ventilnykh i kontaktno-ventilnykh skhemakh – Lupanov - 1956 |
