Completely Reachable Almost Group Automata

TL;DR

This paper investigates the conditions under which a specific class of deterministic automata, characterized by a single defect letter and permutation set, are completely reachable, especially when the permutation group is transitive and imprimitive.

Contribution

It provides new insights into the reachability properties of automata with permutation-generated groups, focusing on transitive imprimitive cases.

Findings

Characterization of complete reachability in automata with permutation groups

Conditions for automata with a defect 1 letter to be completely reachable

Analysis of automata where permutation groups are transitive and imprimitive

Abstract

We consider finite deterministic automata such that their alphabets consist of exactly one letter of defect 1 and a set of permutations of the state set. We study under which conditions such an automaton is completely reachable. We focus our attention on the case when the set of permutations generates a transitive imprimitive group.