Generating Boolean \mu-expressions

In this paper, we consider the class of Boolean -functions, which are the Boolean functions definable by -expressions (Boolean expressions in which no variable occurs more than once). We present an algorithm which transforms a Boolean formulaE into an equivalent -expression-if possible-in time linear in E times , where E is the size ofE andn _m is the number of variables that occur more than once inE. As an application, we obtain a polynomial time algorithm for Mundici's problem of recognizing -functions fromk-formulas 17]. Furthermore, we show that recognizing Boolean -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.