Abstract: Commutativity of quantum automata and commutativity of generalized quantum automata are defined, also commutativity of the language of（generalized） quantum automata is proposed. By using matrix and semigroup, several equivalent characterizations of commutativity of（generalized） quantum automata are obtained. The relationships between commutativity of（generalized） quantum automata and the language of（generalized） quantum automata are studied, and a result is proved that the language of a commutative（generalized） quantum automata is commutative. Moreover, commutativity of general direct product, full direct product, restricted direct product, cascade product and wreath product of（generalized） quantum automata are discussed, and several necessary and sufficient conditions of commutativity of some products of（generalized） quantum automata are obtained.

Key words: quantum automata, generalized quantum automata, commutativity, language, product

摘要： 定义了量子自动机及广义量子自动机的交换性，并提出了（广义）量子自动机所识别语言的交换性。利用半群及矩阵研究（广义）量子自动机的交换性，得出了（广义）量子自动机交换性的几个等价刻画。研究了（广义）量子自动机的交换性与其所识别语言的交换性的关系，证明了交换的（广义）量子自动机所识别的语言也是交换的。此外，讨论了（广义）量子自动机的广义直积、全直积、限制直积、级联积和圈积等积的交换性，得出了一些积的交换性的充分条件和必要条件。

关键词: 量子自动机, 广义量子自动机, 交换性, 语言, 直积