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This paper deals with one-way and two-way weighted automata. When the semiring of weights is commutative, we prove that unambiguous one-way automata, unambiguous two-way automata and deterministic two-way automata realize the same (rational) power series. If the semiring of weights is not commutative, unambiguous one-way automata and deterministic two-way automata realize the same rational power series, but unambiguous two-way automata may realize non rational power series. [ABSTRACT FROM AUTHOR]

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 Büchi automata and introduce a universal automaton for Büchi automata in normal form. We prove that, for every ω-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. [ABSTRACT FROM AUTHOR]