第十次作业-消除左递归
1.将以下文法消除左递归,求FIRST集、FOLLOW集,并分析符号串 i*i+i
E -> E+T | T
T -> T*F | F
F -> (E) | i
消除左递归:
E->TE'
E'->+TE'|ε
T->FT'
T'->*FT'|ε
F->(E) | i
FIRST集:
First((E))={ ( }
First(i)={ i }
First(ε)={ε}
First(*FT')={*}
First(FT')={ (,i }
First(+TE')={+}
First(TE')={ (,i }
FOLLOW集:
Follow(E)={ ) }
Follow(E')={#}
Follow(T)={+,ε}
Follow(T')={#}
Follow(F)={ * ,ε}
SELECT集:
Select(E->TE')=First(TE')={ (,i }
Select(E'->+TE')=First(+TE')={+}
Select(E'->ε)=First(ε)-{ε} U Follow(E')
Select(T->FT')=First(FT')={ (,i }
Select(T'->*FT')=First(*FT')={*}
Select(T'->ε)=First(ε)-{ε} U Follow(T')
Select(F->(E) )=First((E))={ ( }
Select(F->i)=First(i)={ i }
分析符号串 i*i+i
2.P101练习7(2)(3)文法改写,并分别求FIRST集、FOLLOW集,和SELECT集
题目:
(2)A->aABe|a
B->Bb|d
(3)S->Aa|b
A->SB
B->ab
解:(2) A->aA'
A'->aA'Be|ε
B->dB'
B'->bB'|ε
FIRST集:
First(aA')={a}
First(aA'Be)={a}
First(dB')={d}
First(bB')={b}
First(ε)={ε}
FOLLOW集:
Follow(A)={#}
Follow(A')={e}
Follow(B)={e}
Follow(B')={#}
SELECT集:
Select(A->aA')=First(aA')={a}
Select(A'->aA'Be)=First(aA'Be)={a}
Select(B->dB')=First(dB')={d}
Select(B'->bB')=First(bB')={b}
Select(A'->ε)=First(ε)-{ε} U Follow(A')
Select(B'->ε)=First(ε)-{ε} U Follow(B')
(3)先将A、B代入得:S->Saba|b
S->bS'
S'->abaS'
FIRST集:
First(abaS')={a}
First(bS')={b}
FOLLOW集:
Follow(S)={#}
Follow(S')={#}
SELECT集:
Select(S->bS')=First(bS')={b}
Select(S'->abaS')=First(abaS')={a}
求以下文法的FIRST集、FOLLOW集和SELECT集。
(1)S->Ap
A->a |ε
A->cA
A->aA
FIRST集:
First(A)={a,c,ε}
First(Ap)={a,c,p}
First(a)={a}
First(ε)={ε}
First(cA)={c}
First(aA)={a}
FOLLOW集:
Follow(S)={#}
Follow(A)={p}
SELECT集:
Select(S->Ap)=First(Ap)={a,c}
Select(A->a)=First(a)={a}
Select(A->ε)=First(ε)-{ε} U Follow(A)
Select(A->cA)=First(cA)={c}
Select(A->aA)=First(aA)={a}
(2)S->Ap
S->Bq
A->a
A->cA
B->b
B->dB
FIRST集:
First(B)={b,d}
First(A)={a,c}
First(Ap)={a,c}
First(Bq)={b,d}
First(a)={a}
First(cA)={c}
First(b)={b}
First(dB)={d}
FOLLOW集:
Follow(S)={#}
Follow(A)={p}
Follow(B)={q}
SELECT集:
Select(S->Ap)=First(Ap)={a,c}
Select(S->Bq)=First(Bq)={b,d}
Select(A->a)=First(a)={a}
Select(A->cA)=First(cA)={c}
Select(B->b)=First(b)={b}
Select(B->dB)=First(dB)={d}