In this paper, we consider the class of Boolean mu-functions, which ar
e the Boolean functions definable by mu-expressions (Boolean expressio
ns in which no variable occurs more than once). We present an algorith
m which transforms a Boolean formula E into an equivalent mu-expressio
n-if possible-in time linear in parallel to E parallel to times 2(nm),
where parallel to E parallel to is the size of E and n(m) is the numb
er of variables that occur more than once in E. As an application, we
obtain a polynomial time algorithm for Mundici's problem of recognizin
g mu-functions from k-formulas [17]. Furthermore, we show that recogni
zing Boolean mu-functions is co-NP-complete for functions essentially
dependent on all variables and we give a bound close to co-NP for the
general case.