论文标题
关于加权自动机的等效性和最小化的注释
Notes on Equivalence and Minimization of Weighted Automata
论文作者
论文摘要
这套注释在加权自动机上重新提供了已知结果（在一个字段上，也称为多重性自动机）。该文本对数十年来出现在文献中出现的定理和证明的统一观点，并以不同的样式和上下文编写。此处报告的结果都不是新的。内容围绕等效和最小化的基本面，重点是算法方面。演讲是极简主义的。没有尝试激励材料。加权自动机是从线性代数角度观察的。结果，旨在简洁但完整且几乎独立的证明主要依赖于基本线性代数。
This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in different styles and contexts. None of the results reported here are claimed to be new. The content centres around fundamentals of equivalence and minimization, with an emphasis on algorithmic aspects. The presentation is minimalistic. No attempt has been made to motivate the material. Weighted automata are viewed from a linear-algebra angle. As a consequence, the proofs, which are meant to be succinct, but complete and almost self-contained, rely mainly on elementary linear algebra.
