Automata for the mu-calculus and Related Results - Janin, David; Walukiewicz, Igor (BRICS Report Series, 1995)
The propositional mu-calculus as introduced by Kozen in [4] is considered. The notion of disjunctive formula is defined and it is shown that every formula is semantically equivalent to a disjunctive formula. For these formulas many difficulties encountered in the general case may be avoided. For instance, satisfiability checking is linear for disjunctive formulas. This kind of formula gives rise to a new notion of finite automaton which characterizes the expressive power of the mu-calculus over all transition systems.