  A key result in the theory of the modal mu-calculus is the disjunctive normal
form theorem by Janin & Walukiewicz, stating that every mu-calculus formula is
semantically equivalent to a so-called disjunctive formula. These disjunctive
formulas have good computational properties and play a pivotal role in the
theory of the modal mu-calculus. It is therefore an interesting question what
the best normalisation procedure is for rewriting a formula into an equivalent
disjunctive formula of minimal size. The best constructions that are known from
the literature are automata-theoretic in nature and consist of a guarded
transformation, i.e., the constructing of an equivalent guarded alternating
automaton from a mu-calculus formula, followed by a Simulation Theorem stating
that any such alternating automaton can be transformed into an equivalent
non-deterministic one. Both of these transformations are exponential
constructions, making the best normalisation procedure doubly exponential. Our
key contribution presented here shows that the two parts of the normalisation
procedure can be integrated, leading to a procedure that is single-exponential
in the closure size of the formula.
