On the size of disjunctive formulas in the μ-calculus

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