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
解：消除左递归：
(1) E->TE'
E'->+TE'|ε
(2) T->FT'
T'->*FT'|ε
(3) F->(E)|i
① FIRST集：
First(TE') = {T}
First(+TE') = {+}
First(ε) = {ε}
First(FT') = {F}
First(*FT') = {*}
First(ε) = {ε}
First((E)) = {( }
First(i) = {i}
② FOLLOW集：
Follow(E) = {)}
Follow(E') = {#}
Follow(T) = {E'}
Follow(T') = {#}
Follow(F) = {#}
③ SELECT集：
Select(E->TE') = First(TE') = {T}
Select(E'->+TE') = First(+TE') = {+}
Select(E'->ε) = (First(ε) = {ε})∪Follow(E') = {)}
Select(T->FT') = First(FT') = {F}
Select(T'->*FT') = First(+TE') = {*}
Select(T'->ε) = (First(ε) = {ε})∪Follow(T') = {#}
Select( F->(E)) = First((E)) = {( }
Select( F->i) = First(i) = {i}
2.P101练习7（2）（3）文法改写，并分别求FIRST集、FOLLOW集，和SELECT集
(2) A->aABe|a
B->Bb|d
提取左公因子：A->aA' A'->ABe|ε
消除左递归：B->dB' B'->bB'|ε
① FIRST集：
First(aA') = {a}
First(ABe) = {A}
First(ε) = {ε}
First(dB') = {d}
First(bB') = {b}
First(ε) = {ε}
② FOLLOW集：
Follow(A) = {Be}
Follow(A') = {#}
Follow(B) = {e}
Follow(B') = {#}
③ SELECT集：
Select(A->aA') = First(aA') = {a}
Select(A'->ABe) = First(ABe) = {A}
Select(A'->ε) = First(ε) = {ε}∪Follow(A') = {#}
Select(B->dB') = First(dB') = {d}
Select(B'->bB') = First(bB') = {b}
Select(B'->ε) = First(ε) = {ε}∪Follow(B') = {#}
(3) S->Aa|b
A->SB
B->ab
将A->SB代入S->Aa|b可得：S->SBa|b
消除左递归：S->bS' S'->BaS'|ε B->ab
① FIRST集：
First(SBa) = {S}
First(b) = {b}
First(bS') = {b}
First(BaS') = {B}
First(ε) = {ε}
First(ab) = {a}
② FOLLOW集：
Follow(S) = {B}
Follow(S') = {#}
Follow(B) = {a}
③ SELECT集：
Select(S->SBa) = First(SBa) = {S}
Select(S->b) = First(b) = {b}
Select(S->bS') = First(bS') = {b}
Select(S'->BaS') = First(BaS') = {B}
Select(S->ε) = First(ε) = {ε}∪Follow(S') = {#}
Select(B->ab) = First(ab) = {a}
3.课堂练习：
求以下文法的FIRST集、FOLLOW集和SELECT集。
S->Ap
A->a |ε
A->cA
A->aA
① FIRST集：
First(S) = First(Ap) = {a,c,p}
First(a) = {a}
First(ε) = {ε}
First(cA) = {c}
First(aA) = {a}
② FOLLOW集：
Follow(S) = {#}
Follow(A) = {p}
③ SELECT集：
Select(S->Ap)= First(Ap) = {a,c,p}
Select(A->a)= First(a) = {a}
Select(A->ε)= First(ε) = {ε}∪Follow(A) = {p}
Select(A->cA)= First(cA) = {c}
Select(A->aA)= First(aA) = {a}
S->Ap
S->Bq
A->a
A->cA
B->b
B->dB
① FIRST集：
First(S1) = First(Ap) ={a,c}
First(S2) = First(Bq) ={b,d}
First(a) = {a}
First(cA) = {c}
First(b) = {b}
First(dB) = {d}
② FOLLOW集：
Follow(S) = {#}
Follow(A) = {p}
Follow(B) = {q}
③ SELECT集：
Select(S->Ap) = Fisrt(Ap) = {A}
Select(S->Bq) = Fisrt(Bq) = {B}
Select(A->a) = Fisrt(a) = {a}
Select(A->cA) = Fisrt(cA) = {c}
Select(B->b) = Fisrt(b) = {b}
Select(B->dB) = Fisrt(dB) = {d}
