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We examine characteristic features of reversible and quantum computations in the presence of supplementary information, known as advice. In particular, we present a simple, algebraic characterization of languages recognized by one-way reversible finite automata with advice. With a further elaborate argument, a similar but slightly weaker result for bounded-error one-way quantum finite automata is also proven. As an immediate application of those features, we demonstrate certain containments and separations among various standard language families that are suitably assisted by advice.

One-Way Reversible and Quantum Finite Automata with Advice