  In this note, we consider the minimum number of NOT operators in a Boolean
formula representing a Boolean function. In circuit complexity theory, the
minimum number of NOT gates in a Boolean circuit computing a Boolean function
$f$ is called the inversion complexity of $f$. In 1958, Markov determined the
inversion complexity of every Boolean function and particularly proved that
$\lceil \log_2(n+1) \rceil$ NOT gates are sufficient to compute any Boolean
function on $n$ variables. As far as we know, no result is known for inversion
complexity in Boolean formulas, i.e., the minimum number of NOT operators in a
Boolean formula representing a Boolean function. The aim of this note is
showing that we can determine the inversion complexity of every Boolean
function in Boolean formulas by arguments based on the study of circuit
complexity.
