Weak Automata for the Linear Time µ-Calculus

Martin Lange

Abstract: This paper presents translations forth and back between formulas of the linear time μ-calculus and finite automata with a weak parity acceptance condition. This yields a normal form for these formulas, in fact showing that the linear time alternation hierarchy collapses at level 0 and not just at level 1 as known so far. The translation from formulas to automata can be optimised yielding automata whose size is only exponential in the alternation depth of the formula.