Generating Boolean mu-Expressions

Thomas Eiter

Abstract: In this paper, we consider the class of Boolean μ-functions, which are the Boolean functions definable by μ-expressions (Boolean expressions in which no variable occurs more than once). We present an algorithm which transforms a Boolean formulaE into an equivalent μ-expression-if possible-in time linear in ‖E‖ times\(2^{n_m } \), 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 μ-functions fromk-formulas [17]. Furthermore, we show that recognizing Boolean μ-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.