作业十——消除左递归

1.将以下文法消除左递归,并分析符号串 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

答:消除左递归:

  E -> TE'

  E' -> +TE' |  ɛ

  T -> FT'

  T' -> *FT' | ɛ

  F -> (E) | i

   分析符号串i*i+i

 

 

 

   FIRST集合:

  FIRST(TE')={ (, i }

  FIRST(+TE')={+}

  FIRST(ε)={ε}

  FIRST(FT')={ (, i }

  FIRST(*FT')={*}

  FIRST((E))={ ( }

  FIRST(i)={i}

  FOLLOW集:

  FOLLOW(E)={ ),# }

  FOLLOW(E')={ ),# }

  FOLLOW(T)={+,),#}

  FOLLOW(T')={+,),#}

  FOLLOW(F)={*,+,),#}

  SELECT集合:

  SELECT(E->TE')=FIRST(TE')={ (, i }

  SELECT(E'->+TE')=FIRST(+TE')={+}

  SELECT(E'->ε)=FIRST(ε)-{ε}UFOLLOW(E')=FOLLOW(E')={ ),# }

  SELECT(T->FT')=FIRST(FT')={ (,i }

  SELECT(T'->*FT')=FIRST(*FT')={*}

  SELECT(T'->ε)=FIRST(ε)-{ε}UFOLLOW(T')=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

答:文法改写:

  A->aA'

     A'->ABe | ε

  B->dB'

  B'->bB' | ε  

  FIRST集:

  FIRST(aA')={a}

  FIRST(ABe)={a}

  FIRST(ε)={ε}

  FIRST(dB')={d}

  FIRST(bB')={b}

  FOLLOW集:

  FOLLOW(A)={d,#}

  FOLLOW(A')={d,#}

  FOLLOW(B)={e}

  FOLLOW(B')={e}

  SELECT集:

  SELECT(A->aA')=FIRST(aA')={a}

  SELECT(A'->ABe)=FIRST(ABe)={a}

  SELECT(A'->ε)=FIRST(ε)-{ε}UFOLLOW(A')=FOLLOW(A')={d,#}

  SELECT(B->dB')=FIRST(dB')={d}

  SELECT(B'->bB')=FIRST(bB')={b}

  SELECT(B'->ε)=FIRST(ε)-{ε}UFOLLOW(B')=FOLLOW(B')={e}

(3)S -> Aa |b

    A -> SB

    B -> ab

答:文法改写:

  S->bS'

  S'->BaS' | ε

  B->ab 

  FIRST集:

  FIRST(bS')={b}

  FIRST(BaS')={a}

  FIRST(ε)={ε}

  FIRST(ab)={a}

  FOLLOW集:

  FOLLOW(S)={#}

  FOLLOW(S')={#}

  FOLLOW(B)={a}

  SELECT集:

  SELECT(S->bS')=FIRST(bS')={b}

  SELECT(S'->BaS')=FIRST(BaS')={a}

  SELECT(S'->ε)=FIRST(ε)-{ε}UFOLLOW(S')=FOLLOW(S')={#}

  SELECT(B->ab)=FIRST(ab)={a}

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

 答:FIRST集:

  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,p}

  SELECT(A->a)=FIRST(a)={a}

  SELECT(A->ε)=FIRST(ε)-{ε}UFOLLOW(A)=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

 答:FIRST集:

  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->Bp)=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}

posted @ 2019-11-14 20:02  Mr-Lin  阅读(...)  评论(...编辑  收藏