10.30非确定的自动机NFA确定化为DFA

1.设有 NFA M=( {0,1,2,3}, {a,b},f,0,{3} ),其中 f(0,a)={0,1}  f(0,b)={0}  f(1,b)={2}  f(2,b)={3}

   画出状态转换矩阵,状态转换图,并说明该NFA识别的是什么样的语言。

 答:状态转换矩阵:

a

b

0

{0,1}

{0}

1

 

{2}

2

 

{3}

状态转换图:

语言:( a | b )*abb

2.NFA 确定化为 DFA

1.解决多值映射:子集法

1). 上述练习1的NFA

2). P64页练习3

2.解决空弧:对初态和所有新状态求ε-闭包

1). 发给大家的图2

2).P50图3.6

 答:1.(1)

a

b

0

ε{0} = {0}

ε{0} = { 0,1 }

ε{0} = {0}

1

{0,1}

ε{0} = { 0,1 }

ε{1} = {0,2}

2

{0,2}

ε{0} = { 0,1 }

ε{2} = {0,3}

3

{0,3}

ε{0} = { 0,1 }

ε{0} = {0}

 

(2)

 

 

0

1

0

ε{S} = {S}

ε{S} = {VQ}

ε{S} = {QU}

1

ε{VQ}

ε{VQ} = {ZV}

ε{Q} = {QU }

2

ε{QU}

ε{Q} = {V}

ε{QU} = {QUZ}

3

ε{ZV}

ε{ZV} = {Z}

ε{ZV} = {Z}

4

ε{V}

ε{V} = {Z}

 

5

ε{QUZ}

ε{QZ} = {ZV}

ε{QUZ} = {QUZ}

6

ε{Z}

ε{Z} ={Z}

ε{Z} = {Z}


 

2.(1)

 

 

0

1

2

0

ε{A} = {ABC}

ε{A} = {ABC}

ε{B} = {BC}

ε{C} = {C}

1

{BC}

 

ε{B} = {BC}

ε{C} = {C}

2

{C}

 

 

ε{C} = {C}

  

(2)

 

 

a

b

X

ε{0} = {0,1,2,4,7}

ε{3,8} = {1,2,3,4,6,7,8}

ε{5} = {1,2,4,5,6,7}

Y

{1,2,3,4,6,7,8}

ε{3,8} = {1,2,3,4,6,7,8}

ε{5,9} = {1,2,4,5,6,7,9}

Z

{1,2,4,5,6,7}

ε{3,8} = {1,2,3,4,6,7,8}

ε{5} = {1,2,4,5,6,7}

V

{1,2,4,5,6,7,9}

ε{3,8} = {1,2,3,4,6,7,8}

ε{5,10} = {1,2,4,5,6,7,10}

B

{1,2,4,5,6,7,10}

ε{3,8} = {1,2,3,4,6,7,8}

ε{5} = {1,2,4,5,6,7}

 

子集法:

f(q,a)={q1,q2,…,qn},状态集的子集

将{q1,q2,…,qn}看做一个状态A,去记录NFA读入输入符号之后可能达到的所有状态的集合。

步骤:

1).根据NFA构造DFA状态转换矩阵

①确定DFA的字母表,初态(NFA的所有初态集)

②从初态出发,经字母表到达的状态集看成一个新状态

③将新状态添加到DFA状态集

④重复23步骤,直到没有新的DFA状态

2).画出DFA

3).看NFA和DFA识别的符号串是否一致。

原文地址:https://www.cnblogs.com/Azan1999/p/11768971.html