The Cerny conjecture for one-cluster automata with prime length cycle

TL;DR

This paper proves the Cerny conjecture for a specific class of automata with prime length cycles, advancing understanding of automata synchronization and related conjectures.

Contribution

It establishes the conjecture for one-cluster automata with prime length cycles, a significant special case in automata theory.

Findings

Proves the Cerny conjecture for one-cluster automata with prime length cycles

Provides implications for the hybrid Road-coloring-Cerny conjecture in prime cycle digraphs

Advances the theoretical understanding of automata synchronization

Abstract

We prove the Cerny conjecture for one-cluster automata with prime length cycle. Consequences are given for the hybrid Road-coloring-Cerny conjecture for digraphs with a proper cycle of prime length.