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Tree Automata Make Ordinal Theory Easy

Authors: Thierry Cachat

Published in: Dagstuhl Seminar Proceedings, Volume 7441, Algorithmic-Logical Theory of Infinite Structures (2008)

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.

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Thierry Cachat. Tree Automata Make Ordinal Theory Easy. In Algorithmic-Logical Theory of Infinite Structures. Dagstuhl Seminar Proceedings, Volume 7441, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@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/entities/document/10.4230/DagSemProc.07441.6},
  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}
}

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Tree Automata Make Ordinal Theory Easy

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