Job SEVEN - formal style to the regular grammar and Automata
| to sum up |
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| 1, the regular cast as a regular grammar |
Same three rules 1. Rules of the form A → ab converted into A → aB, B → b 2. the form A → a | b rules, be converted into A → a, A → b (A → a | b) 3. The form A → a * b rules, be converted into A → aA, A → b The form A → ba * As a rule, be converted into A → Aa, A → b
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| 2、DFA |
Quintuple There is a unique initial state |
| 3, the three ways described DFA |
Five-tuple, the state diagram (the most intuitive), matrix |
| 4、NFA |
Quintuple Encounters the same state can be converted into a plurality of status symbol In addition to non-empty set of states |
Regular Expression to regular grammar
For any regular formula R selecting a nonterminal Z → Z generation rule R
1. rules of the form A → ab converted into A → aB, B → b
2. the form A → a | b rules, be converted into A → a, A → b (A → a | b)
3. The form A → a * b rules, be converted into A → aA, A → b
The form A → ba * As a rule, be converted into A → Aa, A → b
Continue using the conversion rules, each rule comprising at most until a terminator far.
1(0|1)*101
(a|b)*(aa|bb)(a|b)*
((0|1)*|(11))*
(0|11*0)*
①
Z->A1
A->B0
B->C1
C->1(0|1)*
C->C(0|1)|1
C->C0|C1|1
The idea is for each rule contains up to a terminator, the type 1 (0 | 1) * can be used to convert the third rule, there are 101 regular style is not consistent with the form, you can split it step by step.
②
S->(a|b)S
S->(aa|bb)(a|b)*
S->S(a|b)
S->(aa|bb)
S-> ThE | P | In | SB | AA | BB
A->a
B->b
The idea is if the regular type too long, you first select the most familiar split into formal style form
③
S->((0|1)*|(11))S|ε
S->(0|1)*S|11S|ε
S->(0|1)*S
S->(0|1)S|S
S->0S|1S|S
S->11S
S->1A
A->1S
In summary:
S->0S|1S|S|1A
A->1S
④
(0|11*0)*
S->(0|11*0)S|ε
S->0S|(11*0)S|ε
S->(11*0)S
S->A0
A->11*
A->A1|1
S->0S|A0|ε
A->A1|1
自动机M=({q0,q1,q2,q3},{0,1},f,q0,{q3})
其中f:
(q0,0)=q1
(q1,0)=q2
(q2,0)=q3
(q0,1)=q0
(q1,1)=q0
(q2,1)=q0
(q3,0)=q3
(q3,1)=q3
画现状态转换矩阵和状态转换图。
根据五元组可知，q0,q1,q2,q3是状态，{0,1}是有穷字母表，当状态遇见0或1时会转换到下一个状态，f是映像，q0是唯一的一个初态，{q3}是一个终态集
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|
0 |
1 |
| q0 |
q1 |
q0 |
| q1 |
q2 |
q0 |
| q2 |
q3 |
q0 |
| q3 |
q3 |
q3 |
3.由正规式R 构造 自动机NFA
(a|b)*abb
(a|b)*(aa|bb)(a|b)*
1(1010*|1(010)*1)*0
