Quantum finite automata and linear context-free languages: a decidable problem

TL;DR

This paper proves that it is decidable to determine whether a quantum finite automaton recognizes a language intersecting with a linear context-free language, extending previous results to a broader class of languages.

Contribution

It establishes the recursive decidability of intersection problems between measure once finite quantum automata and linear context-free languages, expanding prior work on free monoids.

Findings

Decidability of intersection problem proven

Extension of previous results to linear context-free languages

Provides a method to analyze quantum automata language recognition

Abstract

We consider the so-called measure once finite quantum automata model introduced by Moore and Crutchfield in 2000. We show that given a language recognized by such a device and a linear context-free language, it is recursively decidable whether or not they have a nonempty intersection. This extends a result of Blondel et al. which can be interpreted as solving the problem with the free monoid in place of the family of linear context-free languages.