Regular functions of infinite words are (partial) functions realized by deterministic two-way transducers with infinite look-ahead. Equivalently, Alur et. al. have shown that they correspond to functions realized by deterministic Muller streaming string transducers, and to functions defined by MSO-transductions. Regular functions are however not computable in general (for a classical extension of Turing computability to infinite inputs), and we consider in this paper the class of deterministic regular functions of infinite words, realized by deterministic two-way transducers without look-ahead. We prove that it is a well-behaved class of functions: they are computable, closed under composition, characterized by the guarded fragment of MSO-transductions, by deterministic Büchi streaming string transducers, by deterministic two-way transducers with finite look-ahead, and by finite compositions of sequential functions and one fixed basic function called map-copy-reverse.
@InProceedings{carton_et_al:LIPIcs.ICALP.2023.121, author = {Carton, Olivier and Dou\'{e}neau-Tabot, Ga\"{e}tan and Filiot, Emmanuel and Winter, Sarah}, title = {{Deterministic Regular Functions of Infinite Words}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {121:1--121:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.121}, URN = {urn:nbn:de:0030-drops-181733}, doi = {10.4230/LIPIcs.ICALP.2023.121}, annote = {Keywords: infinite words, streaming string transducers, two-way transducers, monadic second-order logic, look-aheads, factorization forests} }
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