License: Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2013.502
URN: urn:nbn:de:0030-drops-39605
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/3960/
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Klimann, Ines

The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable

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Abstract

We prove that a semigroup generated by a reversible two-state Mealy automaton is either finite or free of rank 2. This fact leads to the decidability of finiteness for groups generated by two-state or two-letter invertible-reversible Mealy automata and to the decidability of freeness for semigroups generated by two-state invertible-reversible Mealy automata.

BibTeX - Entry

@InProceedings{klimann:LIPIcs:2013:3960,
  author =	{Ines Klimann},
  title =	{{The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{502--513},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Natacha Portier and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/3960},
  URN =		{urn:nbn:de:0030-drops-39605},
  doi =		{10.4230/LIPIcs.STACS.2013.502},
  annote =	{Keywords: Mealy automata, automaton semigroups, decidability of finiteness, decidability of freeness, Nerode equivalence}
}

Keywords: Mealy automata, automaton semigroups, decidability of finiteness, decidability of freeness, Nerode equivalence
Collection: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Issue Date: 2013
Date of publication: 26.02.2013

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