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DOI: 10.4230/LIPIcs.MFCS.2017.56

A Characterisation of Pi^0_2 Regular Tree Languages

Authors: Filippo Cavallari, Henryk Michalewski, and Michal Skrzypczak

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract

We show an algorithm that for a given regular tree language L decides if L is in Pi^0_2, that is if L belongs to the second level of Borel Hierarchy. Moreover, if L is in Pi^0_2, then we construct a weak alternating automaton of index (0, 2) which recognises L. We also prove that for a given language L, L is recognisable by a weak alternating (1, 3)-automaton if and only if it is recognisable by a weak non-deterministic (1, 3)-automaton.

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Filippo Cavallari, Henryk Michalewski, and Michal Skrzypczak. A Characterisation of Pi^0_2 Regular Tree Languages. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 56:1-56:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{cavallari_et_al:LIPIcs.MFCS.2017.56,
  author =	{Cavallari, Filippo and Michalewski, Henryk and Skrzypczak, Michal},
  title =	{{A Characterisation of Pi^0\underline2 Regular Tree Languages}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{56:1--56:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.56},
  URN =		{urn:nbn:de:0030-drops-80683},
  doi =		{10.4230/LIPIcs.MFCS.2017.56},
  annote =	{Keywords: infinite trees, Rabin-Mostowski hierarchy, regular languages}
}

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A Characterisation of Pi^0_2 Regular Tree Languages

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