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International Conference on Foundations of Software Technology and Theoretical Computer Science

FSTTCS 2006: FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science pp 285–296Cite as

Tree Automata Make Ordinal Theory Easy

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4337))

Abstract

We give a new simple proof of the decidability of the First Order Theory of \(({\omega}^{{\omega}^i},+)\) and the Monadic Second Order Theory of (ω 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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Author information

Authors and Affiliations

  1. LIAFA, CNRS UMR 7089 & Université Paris 7, France

    Thierry Cachat

Authors
  1. Thierry Cachat
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Delhi, P.O. Box, 110016, New Delhi, India

    S. Arun-Kumar

  2. Indian Institute of Technology, Delhi

    Naveen Garg

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Cachat, T. (2006). Tree Automata Make Ordinal Theory Easy. In: Arun-Kumar, S., Garg, N. (eds) FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2006. Lecture Notes in Computer Science, vol 4337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944836_27

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  • DOI: https://doi.org/10.1007/11944836_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49994-7

  • Online ISBN: 978-3-540-49995-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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