On Infinite Words Determined by Indexed Languages

We characterize the infinite words determined by indexed languages. An infinite language $L$ determines an infinite word $\alpha$ if every string in $L$ is a prefix of $\alpha$. If $L$ is regular or context-free, it is known that $\alpha$ must be ultimately periodic. We show that if $L$ is an indexed language, then $\alpha$ is a morphic word, i.e., $\alpha$ 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

On Infinite Words Determined by Stack Automata

We characterize the infinite words determined by one-way stack automata. An infinite language L determines an infinite word alpha if every string in L is a prefix of alpha. If L is regular or context-free, it is known that alpha must be ultimately periodic. We extend this result to the class of languages recognized by one-way nondeterministic checking stack automata (1-NCSA). We then consider stronger classes of stack automata and show that they determine a class of infinite words which we call multilinear. We show that every multilinear word can be written in a form which is amenable to parsing. Finally, we consider the class of one-way multihead deterministic finite automata (1:multi-DFA). We show that every multilinear word can be determined by some 1:multi-DFA, but that there exist infinite words determined by 1:multi-DFA which are not multilinear