消除左递归

1.将以下文法消除左递归，分析符号串 i*i+i 。

   并分别求FIRST集、FOLLOW集，和SELECT集

     E -> E+T | T

     T -> T*F | F

     F -> (E) | i

E->TE‘

E‘->+TE‘ | ε

T->FT‘

T‘->*FT‘ | ε

F->I | (E)

 FIRST(TE‘)={I,(}

FIRST(+TE‘)={+}

FIRST(ε)={ε}

FIRST(FT‘)={I,(}

FIRST(*FT‘)={*}

FIRST(I)={I}

FIRST((E))={(}

FOLLOW(E)={)}

FOLLOW(E‘)={#}

FOLLOW(T)={E‘}

FOLLOW(T‘)={#}

FOLLOW(F)={T‘}

SELECT(TE‘)={I,(}

SELECT(+TE‘)={+}

SELECT(ε)={#}

SELECT(FT‘)={I,(}

SELECT(*FT‘)={*}

SELECT(I)={I}

SELECT(F)={(}

2.P101练习7（2）（3）文法改写，并分别求FIRST集、FOLLOW集，和SELECT集

 (2)

 A->aA‘

 A‘->ABe | ε

B->dB‘

B‘->bB‘ | ε

FIRST( aA‘)={a}

FIRST( ABe)={a}

FIRST( ε)={ε}

FIRST(dB‘)={d}

FIRST(bB‘)={b}

FOLLOW(A)={d}

FOLLOW(A‘)={#}

FOLLOW(B)={e}

FOLLOW(B‘)={#}

 SELECT( A->aA‘)={a}

 SELECT( A‘->ABe)={a}

 SELECT( A‘->ε)={#}

 SELECT(B->dB‘)={d}

SELECT(B‘->bB‘)={b}

SELECT(B‘->ε)={#}

(3)

S->bS‘

S‘->BaS‘ | ε

B->ab 

FIRST(bS‘)={b}

FIRST(BaS‘)={a}

FIRST(ε)={ε}

FIRST(ab)={a}

FOLLOW(S)={#}

FOLLOW(S‘)={#}

FOLLOW(B)={a}

SELECT(S->bS‘)={b}

SELECT(S‘->BaS‘)={a}

SELECT(S‘->ε)={#}

 SELECT(B->ab)={a}

课堂练习：

求以下文法的FIRST集、FOLLOW集和SELECT集。

(1)

S->Ap
A->a |ε
A->cA

A->aA

FIRST(Ap)={a,c,p}

FIRST(a)={a}

FIRST(ε)={ε}

FIRST(cA)={c}

FIRST(aA)={a}

FOLLOW(S)={#}

FOLLOW(A)={p}

SELECT(S->Ap)={a,c,p}

SELECT(A->a)={a}

SELECT(A->ε)={p}

SELECT(A->cA)={c}

SELECT(A->aA)={a}

(2)

S->Ap
S->Bq
A->a
A->cA
B->b
B->dB

FIRST(Ap)={a,c}

FIRST(Bq)={b,d}

FIRST(a)={a}

FIRST(c)={c}

FIRST(b)={b}

FIRST(dB)={b}

FOLLOW(S)={#}

FOLLOW(A)={p}

FOLLOW(B)={q}

SELECT(S->Ap)={a,c}

SELECT(S->Bq)={b,d}

SELECT(A->a)={a}

SELECT(A->cA)={c}

SELECT(B->b)={b}

SELECT(B->dB)={d}