1. Elimination left recursive following grammar, the symbol string analyzing i * i + i, respectively, and please FIRST set, FOLLOW sets, and set SELECT
E -> E+T | T
T -> T*F | F
F -> (E) | i
After eliminating left recursion as: E-> TE '
E '-> + T E' | e
T->FT'
T'->*FT'|ε
F->(E)|i
Analysis string of symbols:
FIRST集：
FIRST(TE')={T}
FIRST(+TE')={+}
FIRST (e) = {e}
FIRST(FT')={F}
FIRST(*FT')={*}
FIRST((E))={(}
FIRST(i)={i}
FOLLOW集：
FOLLOW(E)={)}
FOLLOW(E')={#}
FOLLOW(T)={E'}
FOLLOW(T')={#}
FOLLOW(F)={T'}
SELECT set:
SELECT(E→TE')=FIRST(TE')={T}
Select (E '→ + TE) = FIRST (+ TE) = {+}
SELECT (E '→ e) = (FIRST (e) - {e}) ∪FOLLOW (E') = {)}
SELECT(T→FT')=FIRST(FT')={F}
SELECT(T'→*FT')=FIRST(*FT')={*}
SELECT(T'→ε)=(FIRST(ε)-{ε})∪FOLLOW(T')={#}
SELECT(F→(E))=FIRST((E))={(}
SELECT(F→i)=FIRST(i)={i}
Exercise 2.P101 7 (2) (3) is rewritten grammar, please FIRST set respectively, FOLLOW sets, and set SELECT
A->aABe|a
B->Bb|d
Left extract common factor:
A->aA'
A'->ABe|ε
Eliminate left recursion:
B->dB'
B'->bB'|ε
FIRST集：
FIRST(aA')={a}
FIRST(ABe)={A}
FIRST (e) = {e}
FIRST(dB')={d}
FIRST(bB')={b}
FOLLOW集：
FOLLOW(A)={d}
FOLLOW(A')={#}
FOLLOW(B)={e}
FOLLOW(B')={#}
SELECT set:
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')={#}
S->Aa|b
A->SB
B->ab
The progeny obtained by the following two formulas:
S->SBa｜b
Eliminate left recursion:
S →bS'
S '→ BaS' | e
B→ab
FIRST集：
FIRST(SBa)={S}
FIRST(b)={b}
FIRST(bS')={b}
FIRST(BaS)={B}
FIRST (e) = {e}
FIRST(ab)={ab}
FOLLOW集：
FOLLOW(S)={B}
FOLLOW(S')={#}
FOLLOW(B)={a}
SELECT set:
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}
Workshop:
Seeking the following grammar FIRST set, FOLLOW sets and SELECT sets.
S->Ap
A->a |ε
A->cA
A->aA
FIRST集：
FISRT(a)={a}
FIRST (e) = {e}
FIRST(cA)={c}
FIRST(aA)={a}
FIRST(Ap)={a,c,p,ε}
FOLLOW集：
FOLLOW(A)={p}
FOLLOW(S)={#}
SELECT set:
SELECT(S->Ap)=FIRST(Ap)={a,c,p}
SELECT(A->a)=FIRST(a)={a}
SELECT(A->ε)=FIRST(ε)-{ε}υFOLLOW(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
FIRST集：
FIRST(A)={a,c}
FIRST(B)={b,d}
FIRST(S)={a,b,c,d}
FOLLOW集：
FOLLOW(A)={p}
FOLLOW(B)={q}
FOLLOW(S)={#}
SELECT set:
SELECT(S->Ap)=FIRST(Ap)={a,c}
SELECT(S->Bp)=FIRST(Bp)={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}