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.
@InProceedings{smith:LIPIcs.FSTTCS.2013.413, author = {Smith, Tim}, title = {{On Infinite Words Determined by Stack Automata}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)}, pages = {413--424}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-64-4}, ISSN = {1868-8969}, year = {2013}, volume = {24}, editor = {Seth, Anil and Vishnoi, Nisheeth K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.413}, URN = {urn:nbn:de:0030-drops-43692}, doi = {10.4230/LIPIcs.FSTTCS.2013.413}, annote = {Keywords: stack automaton, infinite word, pumping lemma, prefix language, multihead finite automaton} }
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