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  • 10 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

      E -> TE'  

      E' -> +TE'|ε

    T -> T*F | F

      T -> FT'

      T' -> *F|ε

    F -> (E) | i

    1.First集:

    First(TE') = {T}

    First(+TE') = {+}

    First(ε) = {ε}

    First(FT') = {F}

    First(*F) = {*}

    First((E)) = {(}

    First(i) = {i}

    2.Follow集:

    Follow(E) = {)}

    Follow(E') = {ε}

    Follow(T) = {E'}

    Follow(T') ={ε}

    Follow(F) = {ε}

    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' -> *F) = First(*F) = {*}

    Select(T' -> ε) = (First(ε)-{ε})∪Follow(T') = {ε}

    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

    消除公因式:

      B→dB'

      B'→bB'|ε

    1.First集:

    First(aA') = {a}

    First(ABe) = {a}

    First(ε) = {ε}

    First(dB') = {d}

    First(bB') = {b}

    2.Follow集:

    Follow(A) = {Be}

    Follow(A') = {ε}

    Follow(B) = {e}

    Follow(B') = {ε}

    3.Select集:

    Select(A -> aA') = First(aA') = {a}

    Select(A' -> ABe) = First(ABe) = {a}

    Select(A' -> ε) =  (First(ε)-{ε})∪Follow(A')) = {ε}

    Select(B -> dB')= First(dB') = {d}

    Select(B' -> bB') = First(bB') = {b}

    Select(B' -> ε) = (First(ε)-{ε})∪Follow(B')) = {ε}

     (3)

    S -> Aa|b

    A ->SB

    B ->ab

    ②代入①:

      S -> SBa|b

    消除左递归:

      S - > bS'

      S' -> BaS'|ε

      B -> ab

    1.First集:

    First(SBa) = {a}

    First(b) = {b}

    First(bS') = {b}

    First(BaS') = {a}

    First(ε) = {ε}

    First(ab) = {a}

    2.Follow集:

    Follow(S) = {B}

    Follow(S') = {ε}

    Follow(B) = {S'}

    3.Select集:

    Select(S -> SBa) = First(SBa) = {a}

    Select(S -> b) = First(b) = {b}

    Select(S -> bS') = First(bS') = {b}

    Select(S' -> BaS') = First(BaS') = {a}

    Select(S' -> ε) =  (First(ε)-{ε})∪Follow(S')) = {ε}

    Select(B -> ab) = First(ab) = {a}

    3.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) = {a,c,p}

    First(a) = {a}

    First(ε) = {ε}

    First(cA) = {c}

    FIrst(aA) = {a}

    2.Follow集:

    Follow(S) = {ε}

    Follow(A) ={p}

    3.Select集:

    Select(S->Ap) = First(Ap) ={p}

    Select(A -> a) = FIrst(a) = {a}

    Select(A -> ε) = First(ε) = {ε}

    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(Ap) = {a,c}

    First(Bq) = {b,d}

    First(a) = {a}

    First(cA) = {c}

    First(b) = {b}

    First(dB) = {d}

    2.Follow集:

    Follow(S) = {ε}

    Follow(A) = {p}

    Follow(B) = {q}

    3.Select集:

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

    Select(S - >Bq) = First(Bq) = {q}

    Select(A - > a) = First(a) = {a}

    Select(A -> cA) = First(cA) = {c}

    Select(B -> b)= FIrst(b) = {b}

    Select(B ->dB) = FIrst(dB) = {d}

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  • 原文地址:https://www.cnblogs.com/HvYan/p/11840844.html
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