Cerny type automata and rank conjecture
Abstract
The aim of this paper is to prove the Cern\'y conjecture and the rank conjecture for Cern\'y type automata and monoids. A transformation monoid is said to be Cern\'y type if it is generated by a simple idempotent and a regular group of permutations. We prove Cern\'y conjecture for the Cern\'y type synchronizing automata and the rank conjecture for the Cern\'y type transformation monoids. In particular, we obtain the tight bound for the reset threshold of Cern\'y type synchronizing monoids.
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