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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2020.80
URN: urn:nbn:de:0030-drops-127495
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12749/
Rabinovich, Alexander ;
Tiferet, Doron
Ambiguity Hierarchy of Regular Infinite Tree Languages
Abstract
An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is k-ambiguous (for k > 0) if for every input it has at most k accepting computations. An automaton is boundedly ambiguous if there is k ∈ ℕ, such that for every input it has at most k accepting computations. An automaton is finitely (respectively, countably) ambiguous if for every input it has at most finitely (respectively, countably) many accepting computations.
The degree of ambiguity of a regular language is defined in a natural way. A language is k-ambiguous (respectively, boundedly, finitely, countably ambiguous) if it is accepted by a k-ambiguous (respectively, boundedly, finitely, countably ambiguous) automaton. Over finite words every regular language is accepted by a deterministic automaton. Over finite trees every regular language is accepted by an unambiguous automaton. Over ω-words every regular language is accepted by an unambiguous Büchi automaton [Arnold, 1983] and by a deterministic parity automaton. Over infinite trees there are ambiguous languages [Carayol et al., 2010].
We show that over infinite trees there is a hierarchy of degrees of ambiguity: For every k > 1 there are k-ambiguous languages which are not k-1 ambiguous; there are finitely (respectively countably, uncountably) ambiguous languages which are not boundedly (respectively finitely, countably) ambiguous.
BibTeX - Entry
@InProceedings{rabinovich_et_al:LIPIcs:2020:12749,
author = {Alexander Rabinovich and Doron Tiferet},
title = {{Ambiguity Hierarchy of Regular Infinite Tree Languages}},
booktitle = {45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
pages = {80:1--80:14},
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/2020/12749},
URN = {urn:nbn:de:0030-drops-127495},
doi = {10.4230/LIPIcs.MFCS.2020.80},
annote = {Keywords: automata on infinite trees, ambiguous automata, monadic second-order logic}
}
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Keywords: |
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automata on infinite trees, ambiguous automata, monadic second-order logic |
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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 |
