AI 中文总结
从组合视角探索字母变换器等自动机理论，将其转移集视为正交阵列类似物，讨论相关组合编码，用组合结构刻画各类自动机，提出字母变换器同构概念，推广对称性并保持双可逆自动机类别。
AI 中文摘要
本文从类似于拉丁方理论的组合视角探索字母变换器、米利自动机和双可逆自动机的理论。我们将字母变换器的转移集视为正交阵列的类似物，并讨论米利自动机的另外两种类似于拉丁方正交对和(k,n)网的组合编码。我们根据这些组合结构对各类自动机（米利、可逆、可逆、双可逆）进行了刻画。特别地，我们将变换器的反转和对偶化表示为准同构。此外，类似于与拉丁方相关的拟群的同构概念，我们发展了字母变换器的同构概念，它推广了变换器对称性并保持双可逆自动机的类别。
英文摘要
This paper explores the theory of letter transducers, Mealy automata, and bireversible automata from a combinatorial perspective analogous to the theory of Latin squares. We view the sets of transitions of letter transducers as analogs of orthogonal arrays, and discuss two other combinatorial encodings of Mealy automata analogous to orthogonal pairs of Latin squares and to $(k,n)$-nets. We characterize various classes of automata (Mealy, reversible, invertible, bireversible) in terms of these combinatorial structures. In particular, we represent the inversion and dualization of transducers as parastrophisms. Further, similarly to the notion of the isotopisms of the quasigroups associated to Latin squares, we develop the notion of isotopisms of letter transducers generalizing transducer symmetry and preserving the class of bireversible automata.
Comments57 pages, 8 figures
