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On Deciding Topological Classes of Deterministic Tree Languages

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Computer Science Logic (CSL 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3634))

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Abstract

It has been proved by Niwiński and Walukiewicz that a deterministic tree language is either Π\(_{\rm 1}^{\rm 1}\)-complete or it is on the level Π\(_{\rm 3}^{\rm 0}\) of the Borel hierarchy, and that it can be decided effectively which of the two takes place. In this paper we show how to decide if the language recognized by a given deterministic tree automaton is on the Π\(_{\rm 2}^{\rm 0}\), the Σ\(^{\rm 0}_{\rm 2}\), or the Σ\(^{\rm 0}_{\rm 3}\) level. Together with the previous results it gives a procedure calculating the exact position of a deterministic tree language in the topological hierarchy.

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Authors and Affiliations

  1. Institute of Informatics, Warsaw University, ul. Banacha 2, 02 097, Warszawa, Poland

    Filip Murlak

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  1. Filip Murlak
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Editors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, OX1 3QD, Oxford, United Kingdom

    Luke Ong

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© 2005 Springer-Verlag Berlin Heidelberg

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Murlak, F. (2005). On Deciding Topological Classes of Deterministic Tree Languages. In: Ong, L. (eds) Computer Science Logic. CSL 2005. Lecture Notes in Computer Science, vol 3634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538363_30

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  • DOI: https://doi.org/10.1007/11538363_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28231-0

  • Online ISBN: 978-3-540-31897-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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