Some operations over Boolean functions are considered. It is shown that
the operation of the geometrical projection and the operation of the
monotone extension can increase the complexity of Boolean functions for
formulas in each finite basis, for switching networks, for branching
programs, and read-$k$-times branching ... more >>>

We prove that any monotone switching network solving directed connectivity on $N$ vertices must have size $N^{\Omega(\log N)}$

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