One-Way Reversible and Quantum Finite Automata with Advice

TL;DR

This paper explores the capabilities and limitations of one-way reversible and quantum finite automata with advice, providing algebraic characterizations and analyzing the impact of different advice types on language recognition.

Contribution

It offers a simple algebraic characterization of languages recognized by reversible automata with advice and extends similar results to quantum automata, highlighting their power and limitations.

Findings

Algebraic characterization of reversible automata with advice

Containments and separations among language families with advice

Analysis of randomized and quantum advice effects on quantum automata

Abstract

We examine the characteristic features of reversible and quantum computations in the presence of supplementary external information, known as advice. In particular, we present a simple, algebraic characterization of languages recognized by one-way reversible finite automata augmented with deterministic advice. With a further elaborate argument, we prove a similar but slightly weaker result for bounded-error one-way quantum finite automata with advice. Immediate applications of those properties lead to containments and separations among various language families when they are assisted by appropriately chosen advice. We further demonstrate the power and limitation of randomized advice and quantum advice when they are given to one-way quantum finite automata.