Abstract
Motivated by the Cerny conjecture for automata, we introduce the concept of monoidal automata, which allows us the formulation of the Сerny conjecture for monoids. We obtain 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. Keywords: Cerny conjecture, finite automaton, finite monoid, transformation monoid.
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