A lower bound for the monotone depth of connectivity

We show that any monotone circuit for computing graph connectivity must have a depth greater than /spl Omega/((log n)/sup 3/2// log log n). This proves that UCONN/sub n/ is not in monotone NC/sup 1/. The proof technique, which is an adaptation of Razborov's approximation method, is also used to derive lower bounds for a general class of graph problems.<
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