Completely reachable automata: an interplay between automata, graphs, and trees

TL;DR

This paper explores completely reachable automata, where every non-empty state subset can be reached from the entire state set, by characterizing them through graphs and trees to understand their structure.

Contribution

It provides a novel characterization of completely reachable automata using graph and tree structures, linking automata theory with graph theory.

Findings

Characterization of completely reachable automata via graphs and trees

Identification of structural properties that ensure complete reachability

Framework for analyzing automata reachability using combinatorial structures

Abstract

A deterministic finite automaton in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize such automata in terms of graphs and trees.