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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2020.59
URN: urn:nbn:de:0030-drops-127268
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12726/
Kupferman, Orna ;
Leshkowitz, Ofer
On Repetition Languages
Abstract
A regular language R of finite words induces three repetition languages of infinite words: the language lim(R), which contains words with infinitely many prefixes in R, the language ∞ R, which contains words with infinitely many disjoint subwords in R, and the language R^ω, which contains infinite concatenations of words in R. Specifying behaviors, the three repetition languages provide three different ways of turning a specification of a finite behavior into an infinite one. We study the expressive power required for recognizing repetition languages, in particular whether they can always be recognized by a deterministic Büchi word automaton (DBW), the blow up in going from an automaton for R to automata for the repetition languages, and the complexity of related decision problems. For lim R and ∞ R, most of these problems have already been studied or are easy. We focus on R^ω. Its study involves some new and interesting results about additional repetition languages, in particular R^#, which contains exactly all words with unboundedly many concatenations of words in R. We show that R^ω is DBW-recognizable iff R^# is ω-regular iff R^# = R^ω, and there are languages for which these criteria do not hold. Thus, R^ω need not be DBW-recognizable. In addition, when exists, the construction of a DBW for R^ω may involve a 2^{O(n log n)} blow-up, and deciding whether R^ω is DBW-recognizable, for R given by a nondeterministic automaton, is PSPACE-complete. Finally, we lift the difference between R^# and R^ω to automata on finite words and study a variant of Büchi automata where a word is accepted if (possibly different) runs on it visit accepting states unboundedly many times.
BibTeX - Entry
@InProceedings{kupferman_et_al:LIPIcs:2020:12726,
author = {Orna Kupferman and Ofer Leshkowitz},
title = {{On Repetition Languages}},
booktitle = {45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
pages = {59:1--59:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-159-7},
ISSN = {1868-8969},
year = {2020},
volume = {170},
editor = {Javier Esparza and Daniel Kr{\'a}ľ},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12726},
URN = {urn:nbn:de:0030-drops-127268},
doi = {10.4230/LIPIcs.MFCS.2020.59},
annote = {Keywords: B{\"u}chi automata, Expressive power, Succinctness}
}
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Keywords: |
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Büchi automata, Expressive power, Succinctness |
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Collection: |
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45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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18.08.2020 |
