An infinite language L determines an infinite word α if every string in L is a prefix of α. If L is regular, it is known that α must be ultimately periodic; conversely, every ultimately periodic word is determined by some regular language. We investigate other classes of languages to see what infinite words they determine, focusing on languages recognized by various kinds of automata.

Next, we consider prediction of infinite words by automata. In the classic problem of sequence prediction, a predictor receives a sequence of values from an emitter and tries to guess the next value before it appears. The predictor masters the emitter if there is a point after which all of the predictor's guesses are correct. We study the case in which the predictor is an automaton and the emitted values are drawn from a finite set; i.e., the emitted sequence is an infinite word.

The automata we consider are finite automata, pushdown automata, stack automata (a generalization of pushdown automata), and multihead finite automata, and we relate them to purely periodic words, ultimately periodic words, and multilinear words.