More on the complexity of slice functions
Theoretical Computer Science
The monotone circuit complexity of Boolean functions
Combinatorica
The complexity of Boolean functions
The complexity of Boolean functions
Acta Informatica
The complexity of Boolean networks
The complexity of Boolean networks
On the method of approximations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The conjunctive complexity of quadratic Boolean functions
Theoretical Computer Science
On the number of ANDs versus the numbers of ORs in monotone Boolean circuits
Information Processing Letters
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Symmetric approximation arguments for monotone lower bounds without sunflowers
Computational Complexity
Higher lower bounds on monotone size
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On the bottleneck counting argument
Theoretical Computer Science
Counting bottlenecks to show monotone P ? NP
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Potential of the approximation method
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
| Hi-index | 0.00 |
Several results on the monotone circuit complexity and the conjunctive complexity, i.e., the minimal number of AND gates in monotone circuits, of quadratic Boolean functions are proved We focus on the comparison between single level circuits, which have only one level of AND gates, and arbitrary monotone circuits, and show that there is a huge gap between the conjunctive complexity of single level circuits and that of general monotone circuits for some explicit quadratic function Almost tight upper bounds on the largest gap between the single level conjunctive complexity and the general conjunctive complexity over all quadratic functions are also proved Moreover, we describe the way of lower bounding the single level circuit complexity, and give a set of quadratic functions whose monotone complexity is strictly smaller than its single level complexity.