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Documents authored by Klimann, Ines

Document
DOI: 10.4230/LIPIcs.ICALP.2018.131
To Infinity and Beyond

Authors: Ines Klimann

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We prove that if a group generated by a bireversible Mealy automaton contains an element of infinite order, then it must have exponential growth. As a direct consequence, no infinite virtually nilpotent group can be generated by a bireversible Mealy automaton.
Cite as

Ines Klimann. To Infinity and Beyond. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 131:1-131:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{klimann:LIPIcs.ICALP.2018.131,
  author =	{Klimann, Ines},
  title =	{{To Infinity and Beyond}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{131:1--131:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.131},
  URN =		{urn:nbn:de:0030-drops-91359},
  doi =		{10.4230/LIPIcs.ICALP.2018.131},
  annote =	{Keywords: automaton groups, growth of a group, exponential growth}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2016.44
Connected Reversible Mealy Automata of Prime Size Cannot Generate Infinite Burnside Groups

Authors: Thibault Godin and Ines Klimann

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
The simplest example of an infinite Burnside group arises in the class of automaton groups. However there is no known example of such a group generated by a reversible Mealy automaton. It has been proved that, for a connected automaton of size at most 3, or when the automaton is not bireversible, the generated group cannot be Burnside infinite. In this paper, we extend these results to automata with bigger stateset, proving that, if a connected reversible automaton has a prime number of states, it cannot generate an infinite Burnside group.
Cite as

Thibault Godin and Ines Klimann. Connected Reversible Mealy Automata of Prime Size Cannot Generate Infinite Burnside Groups. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{godin_et_al:LIPIcs.MFCS.2016.44,
  author =	{Godin, Thibault and Klimann, Ines},
  title =	{{Connected Reversible Mealy Automata of Prime Size Cannot Generate Infinite Burnside Groups}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{44:1--44:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.44},
  URN =		{urn:nbn:de:0030-drops-64570},
  doi =		{10.4230/LIPIcs.MFCS.2016.44},
  annote =	{Keywords: Burnside problem, automaton groups, reversibility, orbit trees}
}
Document
DOI: 10.4230/LIPIcs.STACS.2013.502
The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable

Authors: Ines Klimann

Published in: LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)

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.
Cite as

Ines Klimann. The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 502-513, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{klimann:LIPIcs.STACS.2013.502,
  author =	{Klimann, Ines},
  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 =	{Portier, Natacha and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.502},
  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}
}
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