One-way quantum finite automata are reversible in nature, which greatly reduces its accepting property. In fact, the set of languages accepted by one-way quantum finite automata is a proper subset of regular languages. In this paper, we replace the tape head of one-way quantum finite automata with DNA double strand and name the model Watson–Crick quantum finite automata. The non-injective complementarity relation of Watson–Crick automata introduces non-determinism in the quantum model. We show that this introduction of non-determinism increases the computational power of one-way quantum finite automata significantly. Watson–Crick quantum finite automata can accept all regular languages and also accepts some languages which are not accepted by any multi-head deterministic finite automata. Exploiting the superposition property of quantum finite automata, we show that Watson–Crick quantum finite automata accept the language L = {ww|w ∈ {a, b} * }.

中文翻译：

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Watson-Crick 量子有限自动机

单向量子有限自动机本质上是可逆的，这大大降低了它的接受性。事实上，单向量子有限自动机接受的语言集是正则语言的一个真子集。在本文中，我们用DNA双链代替单向量子有限自动机的带头，并将模型命名为Watson-Crick量子有限自动机。Watson-Crick 自动机的非单射互补关系在量子模型中引入了非确定性。我们表明，这种非确定性的引入显着提高了单向量子有限自动机的计算能力。Watson-Crick 量子有限自动机可以接受所有常规语言，也可以接受任何多头确定性有限自动机不接受的一些语言。