Monotone circuits for matching require linear depth

We prove that monotone circuits computing the perfect matching function on n-vertex graphs require Ω(n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits. CR categories: F.1.1, Models of Computation, Unbounded Action Devices. ∗This research was partially supported by the American-Israeli Binational Science Foundation grant number 87-00082