1. with NFA M = ({0,1,2,3}, {a, b}, f, 0, {3}), where f (0, a) = {0,1} f (0, b) = {0} f (1, b) = {2} f (2, b) = {3}
State transition matrix shown, state transition diagrams, identification and description of the NFA is what kind of language.
A: The state transition matrix:
|
|
a |
b |
| 0 |
{0,1} |
{0} |
| 1 |
|
{2} |
| 2 |
|
{3} |
State transition diagram:
Language :( a * | b *) abb
2.NFA determine into DFA
1. Solution multifunctions: subset Method
NFA 1). Above the Exercise 1
2). P64 page Exercise 3
2. Empty arc resolved: to find all the initial state and a new state ε- closure
1). Figure 2 distributed to you
2) .P50 3.6 FIG.
A: 1. (1)
|
|
|
a |
b |
| 0 |
e {0} = {0} |
e {0} = {0,1} |
e {0} = {0} |
| 1 |
{0,1} |
e {0} = {0,1} |
e {1} = {0,2} |
| 2 |
{0,2} |
e {0} = {0,1} |
e {2} = {0,3} |
| 3 |
{0,3} |
e {0} = {0,1} |
e {0} = {0} |
（2）
|
|
|
0 |
1 |
| 0 |
e {S} = {S} |
e {S} = {VQ} |
ε {S} = {} QU |
| 1 |
e {VQ} |
ε {VQ} = {} JEH |
ε {Q} = {Q} |
| 2 |
e {QU} |
e {Q} = {V} |
ε {Q} = {} which is |
| 3 |
e {ZV} |
ε {} = {JEH JEH} |
e {ZV} = {Z} |
| 4 |
e {V} |
e {V} = {Z} |
|
| 5 |
e {QUZ} |
e {QZ} = {ZV} |
ε = {{} which is subordinate} |
| 6 |
e {Z} |
e {Z} = {Z} |
e {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 |
e {0} = {0,1,2,4,7} |
e {3,8} = {1,2,3,4,6,7,8} |
e {5} = {1,2,4,5,6,7} |
| Y |
{1,2,3,4,6,7,8} |
e {3,8} = {1,2,3,4,6,7,8} |
e {5,9} = {1,2,4,5,6,7,9} |
| WITH |
{1,2,4,5,6,7} |
e {3,8} = {1,2,3,4,6,7,8} |
e {5} = {1,2,4,5,6,7} |
| V |
{1,2,4,5,6,7,9} |
e {3,8} = {1,2,3,4,6,7,8} |
e {5,10} = {} 1,2,4,5,6,7,10 |
| B |
{1,2,4,5,6,7,10} |
e {3,8} = {1,2,3,4,6,7,8} |
e {5} = {1,2,4,5,6,7} |
Child collection method:
Subset f (q, a) = {q1, q2, ..., qn}, the state set
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。