Representation of (Left) Ideal Regular Languages by Synchronizing Automata

TL;DR

This paper investigates the properties of synchronizing automata and their relation to ideal regular languages, providing bounds and characterizations that advance understanding of reset complexity and language automata correspondence.

Contribution

It establishes a precise lower bound for reset complexity of principal ideal languages and characterizes regular languages with specific synchronizing automata properties.

Findings

Lower bound for reset complexity of principal ideal languages

Connection between principal left ideals and synchronizing automata

Characterization of regular languages with specific reset words

Abstract

We follow language theoretic approach to synchronizing automata and \v{C}ern\'{y}'s conjecture initiated in a series of recent papers. We find a precise lower bound for the reset complexity of a principal ideal languages. Also we show a strict connection between principal left ideals and synchronizing automata. We characterize regular languages whose minimal deterministic finite automaton is synchronizing and possesses a reset word belonging to the recognized language.