Work

Cerny type automata and rank conjecture

Year: 2025

Type: preprint

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

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2501.19166

Author: Rystsov, Igor

Institution: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4407091400

Cites:

Cited by:

Related to: 10