Factorizations and universal automaton of omega languages
Résumé
We extend the concept of factorization on finite words to omega-rational languages and show how to compute them.
We define a normal form for Büchi automata and introduce a universal automaton for Büchi automata in normal form.
We prove that, for every omega-rational language, this Büchi automaton, based on factorization, is canonical and that it is the smallest automaton that contains the morphic image of every equivalent Büchi automaton in normal form.