Compiler theory quiz two jobs - grammar and language

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

　　　　Z->aZb或Z->ab

　　The aZb -> aaZbb or aZb -> aabb

　　~~~~~~~~~~~~~~~~

　　Available so ....... A ^n- B ^n- 

Therefore, G (Z): Z-> aZb | ab definition language is: L (G (the Z)) = {A ^n- B ^n- | n-> =. 1}

 

2. Write grammar quaternion form materials 22 pages identifiers in example 2.2.

  Grammar quad form:

　　Grammar = G (V _N , V _T , P, S)

　　V _n- = {W is (identifier), Q (letters), K (number)}

　　V_t={a,b,c,d...........z,0,1.......9}

　　P={W-->Q | K }

　　S={W}

 

3. Write the following expressions leftmost derivation and rightmost derivation syntax tree.

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, as well as the similarities and differences of the syntax tree.

(1) the most left:

　　E=>E+T=>E+F=>E+i=>T+i=>T*F+i=>T*i+i=>F*i+i=>i*i+i

　 Rightmost derivation

　　E=>E+T=>T+T=>T*F+T=>F*F+T=>i*F+T=>i*i+T=>i*i+F=>i*i+i

　 Derivation Tree:

             

（2）

　  Leftmost derivation:

　　E=>E+T=>T+T=>F+T=>i+T=>i+T*F=>i+F*F=>i+i*F=>i+i*i

　  Rightmost derivation

　　E=>E+T=>E+T*F=>E+T*i=>E+F*i=>E+i*i=>T+i*i=>F+i*i=>i+i*i

　  Derivation Tree:

              

（3）

　  Leftmost derivation:

　　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)

　  Rightmost derivation

　　E=>E+T=>E+F=>E+(E)=>E+(E+T)=>E+(E+F)=>E+(E+i)=>E+(T+i)=>E+(F+i)=>E+(T+i)=>E+(i+i)=>T+(i+i)=>F+(i+i)=>i+(i+i)

　  Derivation Tree: