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Exponentially more concise quantum recognition of nonRMM regular languages
"... We show that there are quantum devices that accept all regular languages and that are exponentially more concise than deterministic finite automata (DFA). For this purpose, we introduce a new computing model of oneway quantum finite automata (1QFA), namely, oneway quantum finite automata together ..."
Abstract

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We show that there are quantum devices that accept all regular languages and that are exponentially more concise than deterministic finite automata (DFA). For this purpose, we introduce a new computing model of oneway quantum finite automata (1QFA), namely, oneway quantum finite automata together with classical states (1QFAC), which extends naturally both measureonce 1QFA and DFA and whose state complexity is upperbounded by both. The original contributions of the paper are the following. First, we show that the set of languages accepted by 1QFAC with bounded error consists precisely of all regular languages. Second, we prove that 1QFAC are at most exponentially more concise than DFA. Third, we show that the previous bound is tight for families of regular languages that are not recognized by measureonce (RMO), measuremany (RMM) and multiletter 1QFA. Fourth, we give a polynomialtime algorithm for determining whether any two 1QFAC are equivalent. Finally, we show that the state minimization of 1QFAC is decidable within EXPSPACE. We conclude the paper by posing some open problems.
Quantum finite automata: A modern introduction?
"... Abstract. We present five examples where quantum finite automata (QFAs) outperform their classical counterparts. This may be useful as a relatively simple technique to introduce quantum computation concepts to computer scientists. We also describe a modern QFA model involving superoperators that is ..."
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Abstract. We present five examples where quantum finite automata (QFAs) outperform their classical counterparts. This may be useful as a relatively simple technique to introduce quantum computation concepts to computer scientists. We also describe a modern QFA model involving superoperators that is able to simulate all known QFA and classical finite automaton variants. 1