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Logic and Program Semantics pp 165–179Cite as

On Topological Completeness of Regular Tree Languages

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7230))

Abstract

We identify the class of \({\bf\Sigma}^{1}_{1}\)–inductive sets studied by Moschovakis as a set theoretical generalization of the class (1,3) of the Rabin-Mostowski index hierarchy of alternating automata on infinite trees. That is, we show that every tree language recognized by an alternating automaton of index (1,3) is \({\bf\Sigma}^{1}_{1}\)–inductive, and exhibit an automaton whose language is complete in this class w.r.t. continuous reductions.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Poland

    Henryk Michalewski

  2. Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Poland

    Henryk Michalewski & Damian Niwiński

Authors
  1. Henryk Michalewski
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  2. Damian Niwiński
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Editor information

Editors and Affiliations

  1. Computer Science Department, Cornell University, 4149 Upson Hall, 14853, Ithaca, NY, USA

    Robert L. Constable

  2. Intelligent Systems Faculty of Science, Institute for Computing and Information Sciences, Radboud University Nijmegen, Postbus 9010, 6500 GL, Nijmegen, The Netherlands

    Alexandra Silva

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Michalewski, H., Niwiński, D. (2012). On Topological Completeness of Regular Tree Languages. In: Constable, R.L., Silva, A. (eds) Logic and Program Semantics. Lecture Notes in Computer Science, vol 7230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29485-3_11

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  • DOI: https://doi.org/10.1007/978-3-642-29485-3_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29484-6

  • Online ISBN: 978-3-642-29485-3

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