On the Intersection Problem for Quantum Finite Automata

TL;DR

This paper investigates the decidability of the intersection problem between languages recognized by measure-once quantum finite automata and those generated by certain types of context-free grammars, extending previous work in quantum automata theory.

Contribution

It provides conditions under which it is decidable to determine if the recognized language and a context-free generated language intersect, advancing understanding of quantum automata language properties.

Findings

Decidability results for intersection problems involving quantum automata and context-free languages.

Extension of previous work on measure-once quantum automata.

Conditions for recursive decidability of language intersection.

Abstract

This paper is a continuation of a previous study on the so-called measure once finite quantum automata model introduced by Moore and Crutchfield in 2000. We investigate conditions assuring that, given a language recognized by such a device and a language generated by a context-free grammar of finite index or by a matrix context-free grammar, it is recursively decidable whether or not they have a nonempty intersection.