Symbolic temporal logic model checking is an automatic verification
method. One of its main features is that a counterexample can be
constructed when a temporal formula does not hold for the model. Most
model checkers so far have restricted the type of formulae that can be
checked and for which counterexamples can be constructed to fair CTL
formulae. This paper shows how counterexamples and witnesses for the
whole µ-Calculus can be constructed. The witness construction
presented in this paper is polynomial in the model and the formula.