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arXiv · 2309.08321

Reset thresholds of transformation monoids

Igor Rystsov·Marek Szykuła
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Abstract

Motivated by the \v{C}ern\'y conjecture for automata, we introduce the concept of monoidal automata, which allows the formulation of the \v{C}ern\'y conjecture for monoids. We show 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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Igor Rystsov, Marek Szykuła. 2023-09-15. Reset thresholds of transformation monoids. https://doi.org/10.1007/s10559-024-00660-z

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