《自動機理論、語言和計算導論》學習第 6 天，p115-p138 總結，總計 24 頁。

一、技術總結

1.associativity and comutativity

(1)commutativity(交換性): Commutativity is the property of an operator that says we can switch the order of its operands and get the same result.

描述的是操作符(operator)的性質。示例：x + y = y + x。

(2)associativity(結合性): Associativity is the property of an operator that allows us to regroup the operands when the operator is applied twice.

描述的是操作符(operator)的性質。示例：(x × y) × z = x × (y × z)。

除了associativity和comutativity，設計的algebraic law有：identities（單位元） & annihilators（零元），distribute law（分配律），idempotent law（冪等律，應用於集合） 。

二、英語總結

1.ad-hoc

ad-(to) + hic(this), to this/for this(specific purpose, particular purpose). p115, There, we gave some ad-hoc arguments why one expression could be replaced by another。

2.analogy vs analog

(1)ana-(according to) + logos(word, speech)。

(2)analogy: c/u. a comparison between things that have similar feature, often used to help explan a idea(類比)。

(3)analog(美式寫法)/analogue(英式寫法)：c. sth that is similar to(類似物)。

p115, However, there are a few places where the analogy breaks down, and there are also some laws that apply to regular expressions but have no analog for arithmetic, especially when the closure operator is involved。

3.adversarial

(1)adversary: ad-(to) + vertere(to turn, see versus)。c. an enemy。

(2)adversarial: adversary + al。adj. involving adversary or opposition。

三、其它

如果你也在看這本書，那咱們可以交流交流。

四、參考資料

1. 編程

(1)Eric S.Roberts，《自動機理論、語言和計算導論(英文版.第3版)》：https://book.douban.com/subject/2274854/

2. 英語

(1)Etymology Dictionary：https://www.etymonline.com

(2) Cambridge Dictionary：https://dictionary.cambridge.org

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