From a theorem of Markov, the minimum number of negation gates in a
circuit sufficient to compute any collection of Boolean functions on
n variable is l=log(n+1). Santha and Wilson
[SIAM Journal of Computing 22(2):294--302 (1993)] show that in some
classes of bounded-depth circuits l negation gates are no
longer sufficient for some explicitly defined Boolean function. In
this paper, we consider a general class of bounded-depth circuits in
which each gate computes an arbitrary monotone Boolean function or
its negation. Our purpose was to extend the theorem of Markov for
such a general class of circuits. We show that a lower bound shown
by Santha and Wilson is an extension of Markov's lower bound after a
small refinement. Moreover, tight upper bounds on the number of
negations for computing an arbitrary collection of Boolean functions
are presented.