License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.07441.6
URN: urn:nbn:de:0030-drops-14082
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2008/1408/
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Cachat, Thierry

Tree Automata Make Ordinal Theory Easy

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07441.CachatThierry.Paper.1408.pdf (0.1 MB)

Abstract

We give a new simple proof of the decidability of the First Order Theory of
$(w^{w^i},+)$ and the Monadic Second Order Theory of $(w^i,<)$, improving the
complexity in both cases. Our algorithm is based on tree automata and a new
representation of (sets of) ordinals by (infinite) trees.


BibTeX - Entry

@InProceedings{cachat:DagSemProc.07441.6,
  author =	{Cachat, Thierry},
  title =	{{Tree Automata Make Ordinal Theory Easy}},
  booktitle =	{Algorithmic-Logical Theory of Infinite Structures},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7441},
  editor =	{Rod Downey and Bakhadyr Khoussainov and Dietrich Kuske and Markus Lohrey and Moshe Y. Vardi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2008/1408},
  URN =		{urn:nbn:de:0030-drops-14082},
  doi =		{10.4230/DagSemProc.07441.6},
  annote =	{Keywords: Ordinals, First Order theory, Monadic Second Order Theory, tree automata}
}

Keywords: Ordinals, First Order theory, Monadic Second Order Theory, tree automata
Collection: 07441 - Algorithmic-Logical Theory of Infinite Structures
Issue Date: 2008
Date of publication: 09.04.2008

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