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

Author Yinfeng Zhu

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Author Details

Yinfeng Zhu
  • Institute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg, Russia

Acknowledgements

I thank Prof. Mikhail V. Volkov for valuable discussions, feedback and research suggestions.

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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) https://doi.org/10.4230/LIPIcs.FSTTCS.2024.34

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • Černý conjecture
  • deterministic finite automaton
  • permutation group
  • reset threshold
  • synchronizing automaton

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