In this paper, we extend the concept of factorization on finite words to ω-rational languages and show how to compute them. We define a normal form for Buchi automata and introduce a universal automaton for Buchi automata in normal form. We prove that, for every ω-rational language, this Buchi automaton, based on factorization, is canonical and that it is the smallest automaton that contains the morphic image of every equivalent Buchi automaton in normal form.
['Vincent Carnino', 'Sylvain Lombardy']
Factorizations and Universal Automaton of Omega Languages