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We consider the so-called measure once finite quantum automata modelintroduced by Moore and Crutchfield in 2000. We show that given a languagerecognized by such a device and a linear context-free language, it isrecursively decidable whether or not they have a nonempty intersection. Thisextends a result of Blondel et al. which can be interpreted as solving theproblem with the free monoid in place of the family of linear context-freelanguages.

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