Cerny type automata and rank conjecture
Formal Languages and Automata Theory
2025-02-03 v1
Abstract
The aim of this paper is to prove the \v{C}ern\'y conjecture and the rank conjecture for \v{C}ern\'y type automata and monoids. A transformation monoid is said to be \v{C}ern\'y type if it is generated by a simple idempotent and a regular group of permutations. We prove \v{C}ern\'y conjecture for the \v{C}ern\'y type synchronizing automata and the rank conjecture for the \v{C}ern\'y type transformation monoids. In particular, we obtain the tight bound for the reset threshold of \v{C}ern\'y type synchronizing monoids.
Keywords
Cite
@article{arxiv.2501.19166,
title = {Cerny type automata and rank conjecture},
author = {Igor Rystsov},
journal= {arXiv preprint arXiv:2501.19166},
year = {2025}
}