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DOI: 10.4230/LIPIcs.MFCS.2016.66
URN: urn:nbn:de:0030-drops-64788
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6478/
Manuel, Amaldev ; Sreejith, A. V.
Two-Variable Logic over Countable Linear Orderings
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Abstract
We study the class of languages of finitely-labelled countable linear orderings definable in two-variable first-order logic. We give a number of characterisations, in particular an algebraic one in terms of circle monoids, using equations. This generalises the corresponding characterisation, namely variety DA, over finite words to the countable case. A corollary is that the membership in this class is decidable: for instance given an MSO formula it is possible to check if there is an equivalent two-variable logic formula over countable linear orderings. In addition, we prove that the satisfiability problems for two-variable logic over arbitrary, countable, and scattered linear orderings are NEXPTIME-complete.
BibTeX - Entry
@InProceedings{manuel_et_al:LIPIcs:2016:6478,
author = {Amaldev Manuel and A. V. Sreejith},
title = {{Two-Variable Logic over Countable Linear Orderings}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {66:1--66:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6478},
URN = {urn:nbn:de:0030-drops-64788},
doi = {10.4230/LIPIcs.MFCS.2016.66},
annote = {Keywords: circ-monoids, countable linear orderings, FO^2}
}
| Keywords: | circ-monoids, countable linear orderings, FO^2 | |
| Seminar: | 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016) | |
| Issue date: | 2016 | |
| Date of publication: | 19.08.2016 |
