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DOI: 10.4230/LIPIcs.MFCS.2022.28
URN: urn:nbn:de:0030-drops-168268
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16826/
Carton, Olivier ; Douéneau-Tabot, Gaëtan
Continuous Rational Functions Are Deterministic Regular
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Abstract
A word-to-word function is rational if it can be realized by a non-deterministic one-way transducer. Over finite words, it is a classical result that any rational function is regular, i.e. it can be computed by a deterministic two-way transducer, or equivalently, by a deterministic streaming string transducer (a one-way automaton which manipulates string registers).This result no longer holds for infinite words, since a non-deterministic one-way transducer can guess, and check along its run, properties such as infinitely many occurrences of some pattern, which is impossible for a deterministic machine. In this paper, we identify the class of rational functions over infinite words which are also computable by a deterministic two-way transducer. It coincides with the class of rational functions which are continuous, and this property can thus be decided. This solves an open question raised in a previous paper of Dave et al.
BibTeX - Entry
@InProceedings{carton_et_al:LIPIcs.MFCS.2022.28,
author = {Carton, Olivier and Dou\'{e}neau-Tabot, Ga\"{e}tan},
title = {{Continuous Rational Functions Are Deterministic Regular}},
booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
pages = {28:1--28:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-256-3},
ISSN = {1868-8969},
year = {2022},
volume = {241},
editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16826},
URN = {urn:nbn:de:0030-drops-168268},
doi = {10.4230/LIPIcs.MFCS.2022.28},
annote = {Keywords: infinite words, rational functions, determinization, continuity, streaming string transducers, two-way transducers}
}
| Keywords: | infinite words, rational functions, determinization, continuity, streaming string transducers, two-way transducers | |
| Seminar: | 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 22.08.2022 |
