双向概率和量子有限自动机的简洁性
Succinctness of two-way probabilistic and quantum finite automata
摘要：
我们证明了双向概率和量子有限自动机（2PFA的和2QFA的）可以比它们的单向版本（1PFA的和1QFA的），和双向非确定性有限自动机（2NFA的）更简洁。为了这个目的，我们证明了几个无限的正则语言的家庭，可以识别一些固定的概率大于$ {1/2} $，通过调整的过渡振幅的2QFA（在一种情况下，2PFA）与一个恒定的状态数，而相应的1PFA的，1QFA的和2NFA的大小增长没有限制。我们还表明，2QFA的混合状态可以支持高效的概率放大。介绍了已知最弱的计算模型，其中量子计算机比经典计算机识别更多的有界错误的语言。
英文摘要：
We prove that two-way probabilistic and quantum finite automata (2PFA's and 2QFA's) can be considerably more concise than both their one-way versions (1PFA's and 1QFA's), and two-way nondeterministic finite automata (2NFA's). For this purpose, we demonstrate several infinite families of regular languages which can be recognized with some fixed probability greater than $ {1/2} $ by just tuning the transition amplitudes of a 2QFA (and, in one case, a 2PFA) with a constant number of states, whereas the sizes of the corresponding 1PFA's, 1QFA's and 2NFA's grow without bound. We also show that 2QFA's with mixed states can support highly efficient probability amplification. The weakest known model of computation where quantum computers recognize more languages with bounded error than their classical counterparts is introduced.
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