We characterize the infinite words determined by indexed languages. An
infinite language L determines an infinite word α if every string in
L is a prefix of α. If L is regular or context-free, it is known
that α must be ultimately periodic. We show that if L is an indexed
language, then α is a morphic word, i.e., α can be generated by
iterating a morphism under a coding. Since the other direction, that every
morphic word is determined by some indexed language, also holds, this implies
that the infinite words determined by indexed languages are exactly the morphic
words. To obtain this result, we prove a new pumping lemma for the indexed
languages, which may be of independent interest.Comment: Full version of paper accepted for publication at MFCS 201