離散點自動生成等高線

有限狀態機 (Finite state machine)

A finite state machine (FSM) is similar to a finite state automation (FSA) except that the finite state machine "prints" an output using an output alphabet distinct from the input alphabet. The final definition is as follow:

有限狀態機(FSM)與有限狀態自動化(FSA)相似，區別在于有限狀態機使用與輸入字母不同的輸出字母“打印”輸出。 最終定義如下：

A finite state machine (also called complete sequential machine ) M( A, S, Z, S0, f, g) consists of six points.

有限狀態機(也稱為完全順序機) M(A，S，Z，S0，f，g)由六個點組成。

A finite set A of input alphabet.

輸入字母的有限集A。

A finite set S of internal state.

內部狀態的有限集S。

A finite set z of output symbol.

輸出符號的有限集z 。

An initial state S0 in S.

在S上的初始狀態S0，

A next-state function f from S X A into S.

從SXA到S的下一狀態函數f 。

An output function g from S X A into Z.

從SXA到Z的輸出函數g 。

有限狀態機的組成 (Components of finite state machine)

Input type

輸入類型

The input type is divided into a square and each square contains a single symbol from the input alphabet X. The end squares of the tape contain end markers at the left end and $ at the right end. The absence of end markers in the input tape indicates that there is an infinite length of the tape. The left to right sequence of symbol between the end markers is the input string to be processed.

輸入類型分為一個正方形，每個正方形包含來自輸??入字母X的單個符號。 磁帶的方格在左端包含結束標記，在右端包含$ 。 輸入磁帶中沒有結束標記，表明磁帶長度無限。 結束標記之間從左到右的符號序列是要處理的輸入字符串。

Reading head

閱讀頭

The head examines only one square at a time and can move on square either to the left or to the right. For further analysis are restrict the movement of R head only to the right side.

頭部一次只檢查一個正方形，并且可以在正方形上向左或向右移動。 為了進一步分析，僅將R頭的移動限制在右側。

Finite control

有限控制

The input to the finite control will be usually symboled under the R-head say a or the present state of the machine say q to give the following output:

有限控制的輸入通常用R頭表示a或機器的當前狀態表示q來表示以下輸出：

A motion of R head along the tape to the next square.

R頭沿磁帶移動到下一個正方形。

The next state of the finite state machine given by & (q, a).

＆(q，a)給出的有限狀態機的下一個狀態。

Transition system

過渡系統

The finite labeled graph in which a state is represented by the vertex or node and the directed edges indicates the transition of a state and the edges are labeled with input/output is known as transition graph or a transition system.

其中狀態由頂點或節點表示且有向邊表示狀態的轉換且邊緣以輸入/輸出標記的有限標記圖稱為轉換圖或轉換系統。

In the normal transition diagram, the initial state is represented by a circle with an arrow pointing towards it, the final state by two concentric circles and the other states are represented by just a circle.

在正常過渡圖中，初始狀態由帶有箭頭的圓形表示，最終狀態由兩個同心圓表示，其他狀態僅由一個圓表示。

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有限自動機的類型 (Types of finite Automata)

There are two types of finite automata:

有限自動機有兩種類型：

1) Deterministic finite automata

1)確定性有限自動機

Some moves of the machine can be uniquely determined by the input symbol and present state. The DFA can be defined with 5 tuples (Q, X, &, q0, F). When,

機器的某些動作可以由輸入符號和當前狀態唯一地確定。 可以使用5個元組(Q，X，＆，q0，F)定義DFA。 什么時候，

• Q - is a finite non-empty set of states.

  Q-是有限的非空狀態集。

• X - is a finite non-empty set of input called input alphabet.

  X-是一個有限的非空輸入集，稱為輸入字母。

• & - is a function which maps Q x X into q and is usually called direct transition function. This is the function which describes the change of states driving the transition. This mapping is usually represented by a transition table or a transition diagram.

  ＆ -是將Q x X映射到q的函數，通常稱為直接轉移函數。 這是描述驅動過渡的狀態變化的功能。 此映射通常由過渡表或過渡圖表示。

• Qo E Q - is the initial state and,

  Qo EQ-是初始狀態，

• F C Q - is the set of final states. It is assumed here that there may be more than one final state.

  FCQ-是最終狀態集。 在此假設最終狀態可能不止一個。

2) Non- deterministic finite Automata

2)非確定性有限自動機

Some moves of the machine can not uniquely determine by the input symbol and present state. The NDFA can be defined with 5 tuples. (Q, X, f, q0, F). Where,

機器的某些動作無法通過輸入符號和當前狀態唯一地確定。 NDFA可以定義為5個元組。 (Q，X，f，q0，F)。 哪里，

• Q - is a finite non-empty set of states.

  Q-是有限的非空狀態集。

• X - is a finite non-empty set of inputs.

  X-是一組有限的非空輸入。

• & - is the transition function mapping from Q x X into 2Q which is the power set of Q, the set of all subset of Q.

  ＆ -是從Q中的過渡函數映射X X成2Q是冪集Q，集合Q的所有子集中的。

• q0 E Q - is the initial state.

  q0 EQ-是初始狀態。

• F C Q - is the set of final states.

  FCQ-是最終狀態集。

The difference between the deterministic and non- deterministic automata is only in &. For deterministic automation, the outcome is a state i.e. an element of Q for non- deterministic automation the outcome is a subset of Q.

確定性自動機與非確定性自動機之間的區別僅在于＆ 。 對于確定性自動化，結果是狀態，即Q的元素；對于非確定性自動化，結果是Q的子集。

翻譯自: https://www.includehelp.com/basics/finite-automata.aspx

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