Answers to Questions Formulated in the Paper "On States Observability in Deterministic Finite Automata"

TL;DR

This paper addresses open questions about state observability in deterministic finite automata, showing that certain language families with limited semi-observable states have specific algebraic properties.

Contribution

It provides definitive answers to open problems regarding the closure properties of regular languages accepted by DFAs with limited semi-observable states.

Findings

Families Tk are anti-AFLs for all k >= 2

T1 family is not closed under Kleene plus

Clarifies the structure of languages accepted by semi-observable state-limited DFAs

Abstract

This paper gives answers to questions formulated as open in the paper "On State Observability in Deterministic Finite Automata" by A. Mateescu and Gh. Paun. Specifically, it demonstrates that for all k >= 2, the families of regular languages acceptable by deterministic finite automata with no more than k semi-observable states, denoted by Tk, are anti-AFL's, and that the family T1 differs in the closure property under Kleene +.