量子有限自动机与加权自动机
Quantum Finite Automata and Weighted Automata
摘要：
量子有限自动机通过利用复值概率振幅中的干涉来获得它们的强度。特别令人感兴趣的是Ambainis和Watrous的双向模型，它具有量子态和经典态（2 QCFA）[A. Ambainis和J. Watrous，具有量子和经典状态的双向有限自动机，理论计算机科学，287（1），pp. 299-311，2002]，因为它结合了恒定大小的量子系统中的干涉功率与双向头的优点。本文是一个步骤，以寻找最强大的模型，这是纯粹的经典，可以模仿量子相位的动力学。我们考虑加权自动机与Cortes-Mohri定义的语言识别[C。Cortes和M. Mohri，Context-Free Recognition with Weighted Automata，Grammars 3（2/3），pp. 133-150，2000]作为模拟2 QCFA的候选模型。给定任何2 QCFA，（i）使用的接受拒绝继续观察，（ii）承认一种语言与单侧错误和（iii）的条目的酉矩阵是代数复数，我们给出了一种方法，构建一个加权自动机在$\mathbb{C}$，有效地模拟它。
英文摘要：
Quantum finite automata derive their strength by exploiting interference in complex valued probability amplitudes. Of particular interest is the 2-way model of Ambainis and Watrous that has both quantum and classical states (2QCFA) [A. Ambainis and J. Watrous, Two-way finite automata with quantum and classical state, Theoretical Computer Science, 287(1), pp. 299-311, 2002], since it combines the advantage of the power of interference in a constant-sized quantum system with a 2-way head. This paper is a step towards finding the least powerful model which is purely classical and can mimic the dynamics of quantum phase. We consider weighted automata with the Cortes-Mohri definition of language recognition [C. Cortes and M. Mohri, Context-Free Recognition with Weighted Automata, Grammars 3(2/3), pp. 133-150, 2000] as a candidate model for simulating 2QCFA. Given any 2QCFA that (i) uses the accept-reject-continue observable, (ii) recognizes a language with one-sided error and (iii) the entries of whose unitary matrices are algebraic complex numbers, we show a method of constructing a weighted automaton over $\mathbb{C}$ that simulates it efficiently.
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