Languages recognized by nondeterministic quantum finite automata

TL;DR

This paper characterizes the class of languages recognized by nondeterministic quantum finite automata (NQFA), showing it equals the class of exclusive stochastic languages and exploring their properties and implications.

Contribution

It provides a complete characterization of languages recognized by NQFA and analyzes their closure properties and relation to classical complexity classes.

Findings

NQFA recognize exactly the exclusive stochastic languages.

The classes recognized by NQFA are invariant across different model variants.

Closure properties of these language classes are established.

Abstract

The nondeterministic quantum finite automaton (NQFA) is the only known case where a one-way quantum finite automaton (QFA) model has been shown to be strictly superior in terms of language recognition power to its probabilistic counterpart. We give a characterization of the class of languages recognized by NQFA's, demonstrating that it is equal to the class of exclusive stochastic languages. We also characterize the class of languages that are recognized necessarily by two-sided error by QFA's. It is shown that these classes remain the same when the QFA's used in their definitions are replaced by several different model variants that have appeared in the literature. We prove several closure properties of the related classes. The ramifications of these results about classical and quantum sublogarithmic space complexity classes are examined.