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DOI: 10.4230/LIPIcs.STACS.2017.39

Pro-Aperiodic Monoids via Saturated Models

Authors: Samuel J. van Gool and Benjamin Steinberg

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Abstract

We apply Stone duality and model theory to study the structure theory of free pro-aperiodic monoids. Stone duality implies that elements of the free pro-aperiodic monoid may be viewed as elementary equivalence classes of pseudofinite words. Model theory provides us with saturated words in each such class, i.e., words in which all possible factorizations are realized. We give several applications of this new approach, including a solution to the word problem for omega-terms that avoids using McCammond's normal forms, as well as new proofs and extensions of other structural results concerning free pro-aperiodic monoids.

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Samuel J. van Gool and Benjamin Steinberg. Pro-Aperiodic Monoids via Saturated Models. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 39:1-39:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{vangool_et_al:LIPIcs.STACS.2017.39,
  author =	{van Gool, Samuel J. and Steinberg, Benjamin},
  title =	{{Pro-Aperiodic Monoids via Saturated Models}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{39:1--39:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.39},
  URN =		{urn:nbn:de:0030-drops-69945},
  doi =		{10.4230/LIPIcs.STACS.2017.39},
  annote =	{Keywords: aperiodic monoids, profinite monoids, Stone duality, saturated models}
}

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Pro-Aperiodic Monoids via Saturated Models

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