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Reset Thresholds of Transformation Monoids

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Cybernetics and Systems Analysis Aims and scope

Abstract

Motivated by the Čherný conjecture for automata, we introduce the concept of monoidal automata, which allows us to formulate the Čherný conjecture for monoids. We obtain the upper bounds on the reset threshold of monoids with certain properties. In particular, we obtain a quadratic upper bound if the transformation monoid contains a primitive group of permutations and a singular of maximal rank with only one point of contraction.

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Authors and Affiliations

  1. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    I. Rystsov

  2. University of Wroclaw, Faculty of Mathematics and Computer Science, Wroclaw, Poland

    M. Szykuła

Authors
  1. I. Rystsov
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  2. M. Szykuła
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Corresponding author

Correspondence to I. Rystsov.

Additional information

This work was supported in part by the National Science Centre, Poland, under project # 2021/41/B/ST6/03691.

Translated from Kibernetyka ta Systemnyi Analiz, No. 2, March–April, 2024, pp. 28–37; DOI https://doi.org/10.34229/KCA2522-9664.24.2.3.

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Rystsov, I., Szykuła, M. Reset Thresholds of Transformation Monoids. Cybern Syst Anal 60, 189–197 (2024). https://doi.org/10.1007/s10559-024-00660-z

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  • DOI: https://doi.org/10.1007/s10559-024-00660-z

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