“δ:Q×Σ→Q"如何变化?是否读过DFA(确定性有限自动机)的定义? [英] How does "δ:Q×Σ→Q" read in the definition of a DFA (deterministic finite automaton)?

问题描述

您怎么说英语δ: Q × Σ → Q?描述×和→的含义也将有所帮助.

How do you say δ: Q × Σ → Q in English? Describing what × and → mean would also help.

推荐答案

δ就像数学函数定义了一组元素到另一组元素的映射.在函数集中，输入参数称为函数的域，而输出则为有效.

A function in mathematical defines mapping of elements in one set to another set. In function set of input arguments are called Domain of a function and output is the rage.

[ANSWER]

在表达式"δ:Q×Σ → Q"中，

×表示笛卡尔积(即一组)，而→是映射.
"δ:Q×Σ → Q"说δ是定义了从Q×Σ到Q的映射的转换函数. 其中，δ的域是Q × Σ，范围是Q.

× means Cartesian product (that is a set), and → is a mapping.
"δ:Q×Σ → Q" says δ is a transition function that defined mapping from Q×Σ to Q. Where, Domain of δ is Q × Σ and Range is Q.

注意:笛卡尔积本身是一种数学模型，它可以两组之间的订单对(映射).

Note: Cartesian Product itself a mathematical that all possible order pair (mapping) between two sets.

您还可以说:

δ是定义状态集Q的笛卡尔积与语言符号Σ到状态集Q之间(或说关联)的映射的转换函数.这是δ的缩写:Q×Σ→Q

δ is a transition function that defined mapping between(or say associates) Cartesian product of set of statesQ and language symbolsΣ into set of stateQ. This is abbreviated by δ: Q×Σ → Q

在这里，Q是状态的有限集合，而Σ是语言符号的有限集合.

Here, Q is finite set of states and Σ is a finite set of language symbols.

此外，您还可以通过任何其他自动化方式以树形方式表示转换函数.
1. 过渡表
2. 过渡图 或说出状态图.
3. 转换功能:一组有限的映射规则.例如{δ(q0, a) → q1，δ(q1, a) → q2}
_{所有出于相同目的定义的映射}

Additionally in any automated you can represent transition function in tree ways.
1. Transition Table
2. Transition graph or say state diagram.
3. Transition function: a finite set of mapping rules. e.g. {δ(q0, a) → q1, δ(q1, a) → q2}
_{All for same purpose define maping}

在DFA中. δ:Q×Σ → Q也可以像δ(Q,Σ) → Q那样编写.它类似于函数.在δ函数中，两个输入参数是状态Q和语言符号Σ，返回值是Q.

In DFA. δ:Q×Σ → Q can also be written like δ(Q,Σ) → Q It's similar to function. In δ function two input arguments are state Q and a language symbol Σ and returned value is Q.

δ(Q,Σ) → Q

假设您的一组转换函数 δ中有一个元素δ(q0, a) → q1，这意味着. 如果当前状态为q0，则可以通过使用a符号来转换为状态q1.以及δ(q0, a) → q1的状态图:

Suppose in your set of transition function δ you have an element δ(q0, a) → q1 this means. If the present state is q0 then by consuming a symbol you can shift to state q1. And the state-diagram for δ(q0, a) → q1:

(q0)---a---►(q1)  

和转换表为:

+----+----+
|Q\Σ | a  |
+----+----+
| q0 | q1 |
+----+----+

都定义了映射(q0, a) to (q1).

某些作者在正式的DFA定义中写δ ⊆ Q×Σ → Q，这意味着δ是 部分功能 (未在完整的域Q×Σ上定义).我们总是可以在整个域上定义δ，这在某些时候是必需的，例如，找到补充DFA. 在这里(互补DFA )，我为同一语言之一是部分DFA，另一种是补充DFA.

Some authors write δ ⊆ Q×Σ → Q in formal DFA definition that means δ is a Partial function (not defined on full Domain Q×Σ). We can always defined δ on the full domain that is required sometime for example to find complement DFA. Here(Complement DFA), I wrote two DFAs for the same language one is partial DFA other is complement DFA.

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