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：
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a |
b |
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|
0 |
{0,1} |
{0} |
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1 |
|
{2} |
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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）
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a |
b |
||
|
0 |
ε{0} = {0} |
ε{0} = { 0,1 } |
ε{0} = {0} |
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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）
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|
|
0 |
1 |
|
0 |
ε{S} = {S} |
ε{S} = {VQ} |
ε{S} = {QU} |
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1 |
ε{VQ} |
ε{VQ} = {ZV} |
ε{Q} = {QU } |
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2 |
ε{QU} |
ε{Q} = {V} |
ε{QU} = {QUZ} |
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3 |
ε{ZV} |
ε{ZV} = {Z} |
ε{ZV} = {Z} |
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4 |
ε{V} |
ε{V} = {Z} |
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5 |
ε{QUZ} |
ε{QZ} = {ZV} |
ε{QUZ} = {QUZ} |
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6 |
ε{Z} |
ε{Z} ={Z} |
ε{Z} = {Z} |
2.（1）
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|
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0 |
1 |
2 |
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0 |
ε{A} = {ABC} |
ε{A} = {ABC} |
ε{B} = {BC} |
ε{C} = {C} |
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1 |
{BC} |
|
ε{B} = {BC} |
ε{C} = {C} |
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2 |
{C} |
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|
ε{C} = {C} |
（2）
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|
|
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。