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URN: urn:nbn:de:0030-drops-14082
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Cachat, Thierry

Tree Automata Make Ordinal Theory Easy

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


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

  author =	{Thierry Cachat},
  title =	{Tree Automata Make Ordinal Theory Easy},
  booktitle =	{Algorithmic-Logical Theory of Infinite Structures},
  year =	{2008},
  editor =	{Rod Downey and Bakhadyr Khoussainov and Dietrich Kuske and Markus Lohrey and Moshe Y. Vardi},
  number =	{07441},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Ordinals, First Order theory, Monadic Second Order Theory, tree automata}

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

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