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DOI: 10.4230/LIPIcs.STACS.2014.530
URN: urn:nbn:de:0030-drops-44853
URL: https://drops.dagstuhl.de/opus/volltexte/2014/4485/
Lohrey, Markus ; Zetzsche, Georg
On Boolean closed full trios and rational Kripke frames
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Abstract
A Boolean closed full trio is a class of languages that is closed under the Boolean operations (union, intersection, and complementation) and rational transductions. It is well-known that the regular languages constitute such a Boolean closed full trio. It is shown here that every such language class that contains any non-regular language already includes the whole arithmetical hierarchy (and even the one relative to this language). A consequence of this result is that aside from the regular languages, no full trio generated by one language is closed under complementation. Our construction also shows that there is a fixed rational Kripke frame such that assigning an arbitrary non-regular language to some variable allows the definition of any language from the arithmetical hierarchy in the corresponding Kripke structure using multimodal logic.
BibTeX - Entry
@InProceedings{lohrey_et_al:LIPIcs:2014:4485,
author = {Markus Lohrey and Georg Zetzsche},
title = {{On Boolean closed full trios and rational Kripke frames}},
booktitle = {31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
pages = {530--541},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-65-1},
ISSN = {1868-8969},
year = {2014},
volume = {25},
editor = {Ernst W. Mayr and Natacha Portier},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2014/4485},
URN = {urn:nbn:de:0030-drops-44853},
doi = {10.4230/LIPIcs.STACS.2014.530},
annote = {Keywords: rational transductions, full trios, arithmetical hierarchy, Boolean operations}
}
| Keywords: | rational transductions, full trios, arithmetical hierarchy, Boolean operations | |
| Seminar: | 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014) | |
| Issue date: | 2014 | |
| Date of publication: | 05.03.2014 |
