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A Quadratic Upper Bound on the Reset Thresholds of Synchronizing Automata Containing a Transitive Permutation Group

Authors: Yinfeng Zhu

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)


Abstract
For any synchronizing n-state deterministic automaton, Černý conjectures the existence of a synchronizing word of length at most (n-1)². We prove that there exists a synchronizing word of length at most 2n² - 7n + 7 for every synchronizing n-state deterministic automaton that satisfies the following two properties: 1. The image of the action of each letter contains at least n-1 states; 2. The actions of bijective letters generate a transitive permutation group on the state set.

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Yinfeng Zhu. A Quadratic Upper Bound on the Reset Thresholds of Synchronizing Automata Containing a Transitive Permutation Group. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 34:1-34:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{zhu:LIPIcs.FSTTCS.2024.34,
  author =	{Zhu, Yinfeng},
  title =	{{A Quadratic Upper Bound on the Reset Thresholds of Synchronizing Automata Containing a Transitive Permutation Group}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{34:1--34:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.34},
  URN =		{urn:nbn:de:0030-drops-222236},
  doi =		{10.4230/LIPIcs.FSTTCS.2024.34},
  annote =	{Keywords: \v{C}ern\'{y} conjecture, deterministic finite automaton, permutation group, reset threshold, synchronizing automaton}
}
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