The class of languages recognizable by 1-way quantum finite automata is not closed under union

TL;DR

This paper investigates quantum finite automata (QFA), revealing that the class of languages they recognize is not closed under union or any Boolean operations, highlighting fundamental differences from classical automata.

Contribution

It demonstrates that the class of languages recognized by QFA is not closed under union or any Boolean operations, advancing the theoretical understanding of QFA capabilities.

Findings

QFA cannot recognize all regular languages

The class of QFA-recognizable languages is not closed under union

QFA are limited in Boolean operations compared to classical automata

Abstract

In this paper we develop little further the theory of quantum finite automata (QFA). There are already few properties of QFA known, that deterministic and probabilistic finite automata do not have e.g. they cannot recognize all regular languages. In this paper we show, that class of languages recognizable by QFA is not closed under union, even not under any Boolean operation, where both arguments are significant.