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Wirth–Weber precedence relationship

The Wirth–Weber belgilar juftligi o'rtasidagi munosabatlar ${ displaystyle (V_ {t} kubok V_ {n})}$ a ekanligini aniqlash uchun zarur rasmiy grammatika a oddiy ustunlik grammatikasiva bunday holatda oddiy ustunlik tahlilchisi foydalanish mumkin.

Maqsad qachon ekanligini aniqlashdir yashovchan prefikslar bor pivot va kamaytirilishi kerak. A ${ displaystyle gtrdot}$ degan ma'noni anglatadi pivot topildi, a ${ displaystyle lessdot}$ potentsial degani pivot boshlanadi va a ${ displaystyle doteq}$ demak, biz hali ham o'sha holatdamiz pivot.

Rasmiy ta'rif

{ displaystyle G = langle V_ {n}, V_ {t}, S, P rangle}

{ displaystyle { begin {aligned} X doteq Y & iff { begin {case} A to alfa XY beta in P A in V_ {n} alfa, beta in (V_ {n} chashka V_ {t}) ^ {*} X, Y in (V_ {n} stakan V_ {t}) end {case}} X lessdot Y & iff { begin {case} A to alfa XB beta in P B Rightarrow ^ {+} Y gamma A, B in V_ {n} alfa, beta, gamma in (V_ {n} cup V_ {t}) ^ {*} X, Y in (V_ {n} cup V_ {t}) end {case}} X gtrdot a & iff { begin {case} A to alfa BY beta in P B Rightarrow ^ {+} gamma X Y Rightarrow ^ {*} a delta A, B in V_ { n} alfa, beta, gamma, delta in (V_ {n} kubok V_ {t}) ^ {*} X, Y in (V_ {n} kubok V_ {t) }) a in V_ {t} end {case}} end {aligned}}}

Birinchi darajali munosabatlar hisoblash algoritmi

Belgilar uchun uchta to'plamni aniqlaymiz:

{ displaystyle { begin {aligned} mathrm {Head} ^ {+} (X) & = {Y mid X Rightarrow ^ {+} Y alpha } mathrm {Tail} ^ {+ } (X) & = {Y mid X Rightarrow ^ {+} alfa Y } mathrm {Head} ^ {*} (X) & = ( mathrm {Head} ^ {+} ( X) cup {X }) cap V_ {t} end {hizalangan}}}

Bosh^*(X) X agar X terminaldir va agar bo'lsa X terminal emas, bosh^*(X) faqat Head-ga tegishli bo'lgan terminallar to'plamidir⁺(X). Ushbu to'plam tengdir Birinchi to'plam yoki Fi (X) tasvirlangan LL tahlilchisi.

Bosh⁺(X) va quyruq⁺(X) agar ∅ bo'lsa X terminaldir.

Hisoblash munosabatlari uchun psevdokod:

RelationTable: = ∅
Har bir ishlab chiqarish uchun ${ displaystyle A to alpha in P}$ ${ displaystyle A to alpha in P}$
- Har ikkala qo'shni belgi uchun X Y yilda a
  - qo'shish (RelationTable, ${ displaystyle X doteq Y}$ )
  - qo'shish (RelationTable, ${ displaystyle X lessdot mathrm {Head} ^ {+} (Y)}$ )
  - qo'shish (RelationTable, ${ displaystyle mathrm {Tail} ^ {+} (X) gtrdot mathrm {Head} ^ {*} (Y)}$ )
qo'shish (RelationTable, ${ displaystyle $ lessdot mathrm {Head} ^ {+} (S)}$ ) qayerda $S$ grammatikaning boshlang'ich bo'lmagan terminali, $ esa chegara belgisi
qo'shish (RelationTable, ${ displaystyle mathrm {Tail} ^ {+} (S) gtrdot $}$ ) qayerda $S$ grammatikaning boshlang'ich bo'lmagan terminali, $ esa chegara belgisi

${ displaystyle lessdot}$ va ${ displaystyle gtrdot}$ ular o'rniga belgilangan elementlar o'rniga to'plamlar bilan ishlatiladi, bu holda siz barchasini qo'shishingiz kerak kartezian mahsuloti to'plamlar / elementlar o'rtasida.

Misollar

${ displaystyle S dan aSSb | c} ga$

Bosh⁺(a) = ∅
Bosh⁺(S) = {a, v}
Bosh⁺(b) = ∅
Bosh⁺(v) = ∅
Quyruq⁺(a) = ∅
Quyruq⁺(S) = {b, v}
Quyruq⁺(b) = ∅
Quyruq⁺(v) = ∅
Bosh^*(a) = a
Bosh^*(S) = {a, v}
Bosh^*(b) = b
Bosh^*(v) = v
${ displaystyle S - aSSb}$ ${ displaystyle S - aSSb}$
- a Ning yonida S
  - ${ displaystyle a doteq S}$
  - ${ displaystyle a lessdot mathrm {Head} ^ {+} (S)}$ ${ displaystyle a lessdot mathrm {Head} ^ {+} (S)}$
    - ${ displaystyle a lessdot a}$
    - ${ displaystyle a lessdot c}$
- S Ning yonida S
  - ${ displaystyle S doteq S}$
  - ${ displaystyle S lessdot mathrm {Head} ^ {+} (S)}$ ${ displaystyle S lessdot mathrm {Head} ^ {+} (S)}$
    - ${ displaystyle S lessdot a}$
    - ${ displaystyle S lessdot c}$
  - ${ displaystyle mathrm {Tail} ^ {+} (S) gtrdot mathrm {Head} ^ {*} (S)}$ ${ displaystyle mathrm {Tail} ^ {+} (S) gtrdot mathrm {Head} ^ {*} (S)}$
    - ${ displaystyle b gtrdot a}$
    - ${ displaystyle b gtrdot c}$
    - ${ displaystyle c gtrdot a}$
    - ${ displaystyle c gtrdot c}$
- S Ning yonida b
  - ${ displaystyle S doteq b}$
  - ${ displaystyle mathrm {Tail} ^ {+} (S) gtrdot mathrm {Head} ^ {*} (b)}$ ${ displaystyle mathrm {Tail} ^ {+} (S) gtrdot mathrm {Head} ^ {*} (b)}$
    - ${ displaystyle b gtrdot b}$
    - ${ displaystyle c gtrdot b}$
${ displaystyle S dan c}$ ${ displaystyle S to c}$
- faqat bitta belgi bor, shuning uchun hech qanday munosabat qo'shilmaydi.

ustunlik jadvali: ${ displaystyle { begin {array} {c | ccccc} & S & a & b & c & $ hline S & doteq & lessdot & doteq & lessdot & a & doteq & lessdot && lessdot & b && gtrdot & gtrdot & gtrdot & gtrdot c && gtrdot & gtrdot & gtrdot & gtrdot $ && lessdot && lessdot & end {array}}}$

Qo'shimcha o'qish

Aho, Alfred V.; Ullman, Jeffri D., Tahlil, tarjima va kompilyatsiya nazariyasi

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