研究报告：双向量子有限自动机上操作的状态复杂性
Research report: State complexity of operations on two-way quantum finite automata
摘要：
本文讨论了最小{ \it双向量子有限自动机}（2 qfa）对每个固定长度的所有输入进行操作所需的大小复杂性。这种复杂性度量，称为操作的状态复杂性，在测量转换语言所需的信息量时很有用。我们专注于交叉，联盟，反转，和连锁业务，并显示一些上界的操作状态复杂性的2 QFA的。此外，我们提出了一些非正则语言，并证明这些语言可以接受的2 qfa的线性时间内的单侧错误概率。值得注意的是，这些例子表明，我们为这些操作获得的边界并不紧，因此值得改进。通过一个实例说明了双向可逆有限自动机模拟单向确定有限自动机的状态数的上界一般是不紧的。
英文摘要：
This paper deals with the size complexity of minimal {\it two-way quantum finite automata} (2qfa's) necessary for operations to perform on all inputs of each fixed length. Such a complexity measure, known as state complexity of operations, is useful in measuring how much information is necessary to convert languages. We focus on intersection, union, reversals, and catenation operations and show some upper bounds of state complexity of operations on 2qfa's. Also, we present a number of non-regular languages and prove that these languages can be accepted by 2qfa's with one-sided error probabilities within linear time. Notably, these examples show that our bounds obtained for these operations are not tight, and therefore worth improving. We give an instance to show that the upper bound of the state number for the simulation of one-way deterministic finite automata by two-way reversible finite automata is not tight in general.
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