2. The second working language comprehension and grammar

1. understood that symbol string and set operations.

L={A,B, … ,Z,a,b, … ,z}

D={0,1, … ,9}

Description meaning under represented:

LUD

LD

L4

L*

D+

L (LUD) *

 

LUD: full set of letters and numbers

LD: a letter followed by a set of digits

L4: the set of all strings of symbols of four-letter

L *: the set of all strings of symbols of the alphabet

Symbol string or a set of several digits: D +

L * (LUD): the set of all strings beginning with the letter symbols, followed by the letter, numbers.

 

2. grammar G (Z): Z-> aZb | ab definition of what kind of language?

Z->ab

Z->aZb ->aabb

Z ->aZb ->aaZbb ->aaabbb

Therefore, the definition is A ^n- B ^n-.

 

3. Write grammar quaternion form materials 22 pages in Example 2.2 identifier (VN, NT, P, S).

I->

L->

D->

 

V_N={I,L,D}

V_T={L,D}

P={I->L,I->IL,I->ID,L->L,D->D}

S={I}

 

4. Write the following expressions leftmost derivation, rightmost derivation.

G (E):

E=> E + T | T

T=>T * F | F

F=>（E）| i

• i*i+i
• i+i*i
• i+(i+i)

 Observe different leftmost and rightmost derivation process.

 

i*i+i：

最左推导：E=>E+T=>T+T=>T*F+T=>F*F+T=>i*F+T=>i*i+T=>i*i+F=>i*i+i

最右推导：E=>E+T=>E+F=>E+i=>T+i=>T*F+i=>T*i+i=>F*i+i=>i*i+i

i+i*i：

最左推导：E=>E+T=>T+T=>F+T=>i+T=>i+T*F=>i+F*F=>i+i*F=>i+i*i

最右推导：E=>E+T=>E+T*F=>E+T*i=>E+F*i=>E+i*i=>T+i*i=>F+i*i=>i+i*i

i+(i+i)：

最左推导：E=>E+T=>T+T=>F+T=>i+T=>i+F=>i+(E)=>i+(E+T)=>i+(T+T)=>i+(F+T)=>i+(i+T)=>i+(i+F)=>i+(i+i)

最右推导：E=>E+T=>E+F=>E+(E)=>E+(E+T)=>E+(E+F)=>E+(E+i)=>E+(T+i)=>E+(F+i)=>E+(i+i)=>T+(i+i)=>F+(i+i)=>i+(i+i)