The complexity of Boolean functions
The complexity of Boolean functions
Monotone circuits for connectivity require super-logarithmic depth
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Monotone circuits for matching require linear depth
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Some Exact Complexity Results for Straight-Line Computations over Semirings
Journal of the ACM (JACM)
Lower bounds on arithmetic circuits via partial derivatives
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Multi-linear formulas for permanent and determinant are of super-polynomial size
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Memory bounds for recognition of context-free and context-sensitive languages
FOCS '65 Proceedings of the 6th Annual Symposium on Switching Circuit Theory and Logical Design (SWCT 1965)
On the incompressibility of monotone DNFs
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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A monotone boolean circuit is said to be multilinear if for any AND gate in the circuit, the minimal representation of the two input functions to the gate do not have any variable in common. We show that multilinear boolean circuits for bipartite perfect matching require exponential size. In fact we prove a stronger result by characterizing the structure of the smallest multilinear boolean circuits for the problem. We also show that the upper bound on the minimum depth of monotone circuits for perfect matching in general graphs is O(n).