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 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 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. 1998 ACM Subject Classification F.1.1 Models of Computation, F.4.3 Formal Languages