()

4.1 4.1.1G[S]: SaBC Bib|b CDE|FG|c Dd Eeh Fde Gt abdet

PPPP=+=>P, G1S SpA SqB AcAd AaW=pccadd, S =>pA=>pcAd=>pccAdd=>pccadd

G2[S]SAp SBq Aa AcA Bb BdBW=ccap, S=>Ap=>cAp=>ccAp=>ccap

G3[S]SaA Sd AbAS AW=abd,abd S=>aA=>abAS=>abS=>abd

4.1.2 1. ,AA=+=>AAA(1) a. EE+T|T ET+E|Tb.EE+T|T TT*F|F F(E)|i ETE E+TE| TFT T*FT| F(E)|i

AA1|A2|A3||Am|1|2|3||nA1 A|2 A|3 A||nAA 1 A|2 A|3 A||m A| SSS*|SS+|aSaS S S*S| S+S|

(2) (P=+=>P)a.A1,A2,A3,,Anb.for(i=1;i

SAa|b AAc|Sd|A1=S A2=A SAa|b AAc| Aa|bd|SAa|b AAc|ad|bd|SAa|b AbdA|A AcA|adA| 2. PP1|2|3||na,a

Sif E then S|if E then S else S|bSif E then S S|bSelse S| A1|2|3||n| AA| A1|2|3||nG[S]:SaBC Bib|b CDE|FG|c Dd Eeh Fde Gt SaBC Bib|b CdC|c CeE Eh|G Gt

G[S]SaSd SAc AaS AbSaSd SaSc Sbc SaSS Sbc Sd|cG[S]SAp|Bq AaAp|d BaBq|eL[G]={andpn+1ameqm+1|m,n0}mna

G[E] EE+T|T TT*F|F FE|i ETE E+TE| TFT T*FT| F(E)|i

void E() {T()E(); }void E() {if(==+) {() T()E(); } }

void T() { F()T(); } void T() {if(==*) {() F()T(); } }

void F() { if(==i) (); else if(==() {()E() if(==)) (); else (); } else () }

,BNF,:ET{+T} TF{*F) F(E)|i :void E() {T() while(==+) {() T(); } }void T() {F() while(==*) {() F(); } }

void F() { if(==i) (); else if(==() {()E() if(==)) (); else (); } else () }

(1)(2)(3)

4.1.4 ,,LL1 LLKLL1K

1.LL(1) LL1

1 LL(1)M[Aa]A a##M[Aa]AaA2 #

3 Xa#SXaa.XVt {#} X=a=# X=a#X

Xab.XVnXaMM[Xa]M[Xa]XXXM[Xa]

ETE E+TE| TFT T*FT| F(E)|i

i+*()#EETEETEEE+TEEETTFTTFTTTT*FTTTFFiF(E)

0 #E i*(i+i)+i# ETE1 #ET i*(i+i)+i# TFT2 #ETF i*(i+i)+i# Fi3 #ETi i*(i+i)+i# i4 #ET *(i+i)+i# T *F T 5 #ETF* *(i+i)+i# *6 #ETF (i+i)+i# F(E)7 #ET)E( (i+i)+i# (8 #ET)E i+i)+i# ETE9 #ET)ET i+i)+i# TFT

10 #ET)ETF i+i)+i# Fi11 #ET)ETi i+i)+i# i12 #ET)ET +i)+i# T 13 #ET)E +i)+i# E +TE14 #ET)ET+ +i)+i# +15 #ET)ET i)+i# TFT16 #ET)ETF i)+i# Fi17 #ET)ETi i)+i# i 18 #ET)ET )+i# T 19 #ET)E )+i# E

20 #ET) )+i# )21 #ET +i# T 22 #E +i# E +TE 23 #ET+ +i# +24 #ET i# TFT25 # ET F i# Fi26 # ET i i# i 27 # ET # T 28 # E # E 29 # #

2. LL(1)4-1 FIRST()={a|=+=>a...,aVt} =*=>FIRST() AAijFIRST(i) FIRST(j)=AAa,FIRST()AaAAFOLLOW4-2 FOLLOWA={a|S=*=>...Aa...,aVt}S=*=>...A#FOLLOWA

Aiji=*=>FIRST(i)FIRST()FOLLOWA4-3 A=*=>,SELECT(A)=FIRST()-{ }FOLLOWA,SELECT(A)= FIRST()

LL1AAiAj SELECTAi SELECTAj=ij

LL11LL1LL12LL1 LL1 LL1LL1LL1

FIRST XVtVn,FIRSTXFIRST1XVtFIRSTX={X}2XVnXa...aFIRSTXXFIRSTXXY...YVnFIRSTYFIRSTXXY1Y2Y3...YkY1Y2Y3...Yi-1 j1ji-1, FIRSTYiY1Y2Y3...Yi-1=*=>,FIRSTYiFIRSTYiFIRSTXFIRSTYij=1,2,3...,k,FIRST(X)

X1X2X3...XnFIRST FIRSTX1FIRSTX1X2X3...XnFIRSTX1FIRSTX2FIRSTX1FIRSTX2FIRSTX3FIRSTX1X2X3...XniFIRSTXiFIRSTX1X2X3...Xn

FOLLOW GAFOLLOWA#FOLLOWA1S# FOLLOWA2ABFIRSTFOLLOW(B)3ABAB=*=>(FIRST)FOLLOWAFOLLOWB

SELECT ASELECTAFIRSTSELECTA=FIRST()-{}FOLLOWA,SELECT(A)= FIRST()

G[S]SAB SbC A Ab B BaD CAD Cb DaS DcFIRSTFOLLOWSELECTFIRST(S)={a,b,}FIRST(A)={b,}FIRST(B)={a,}FIRST(C)={a,b,c}FIRST(D)={a,c}

FIRST(AB)={a,b,} FIRST(bC)={b} FIRST()={} FIRST(b)={b} FIRST(aD)={a} FIRST(b)={b} FIRST(aS)={a} FIRST(c)={c} FOLLOW(S)={#} FOLLOW(A)={a,#,c} FOLLOW(B)={#} FOLLOW(C)={#} FOLLOW(D)={#}

SELECT(SAB)={a,b,#} SELECT(SbC)={b} SELECT(A)={a,c,#} SELECT(Ab)={b} SELECT(B)={#} SELECT(BaD)={a} SELECT(CAD)={a,b,c} SELECT(Cb)={b} SELECT(DaS)={a} SELECT(Dc)={c}

G[E]ETE E+TE| TFT T*FT| F(E)|iFIRSTFOLLOWSELECTFIRST(E)={(,i} FIRST(E)={+,} FIRST(T)={(,i} FIRST(T)={*,} FIRST(F)= {(,i} FOLLOW(E)={#,)} FOLLOW(E)={#,)} FOLLOW(T)={#,),+} FOLLOW(T)={#,),+} FOLLOW(F)={#,),+,*}

SELECT(ETE)={(,i}SELECT(E+TE)={+}SELECT(E)= {#,)}SELECT(TFT)={(,i}SELECT(T*FT)={*} SELECT(T)= {#,),+}SELECT(F(E))= {(}SELECT(Fi)={i}

1SELECT2#a aSELECT(A),AM[A,a]3M[A,a]FIRSTFOLLOWSELECT

i+*()#EETEETEEE+TEEETTFTTFTTTT*FTTTFFiF(E)

LL1G[S]Sif E then S S|a Selse S| Eb FIRST(S)={if} FIRST(S)={else,} FIRST(E)={b} FOLLOW(S)={else,#} FOLLOW(S)={else,#} FOLLOW(E)={then} SELECT(Sif E then S S)={if} SELECT(Sa)={a} SELECT(Selse S)={else} SELECT(S)={else,#} SELECT(Eb)={b}

M[s,else]S

abelseifthen#SSaSif E then S SSSelse S SSEEb

4.2 .4.2.1 (1) (2) # # a1a2a3a4...an#

#S #SG[S]SaAcBe Ab AAb Bdabbcde

1#abbcde#2#abbcde#3#abbcde#Ab4#aAbcde#5#aAbcde#AAb6#aAcde#7#aAcde#8#aAcde#Bd9#aAcBe#10#aAcBe#SaAcBe11#S#

1. 4-4 XY XY X>Y XYX ,< XY GXY XY X>Y GBD,B=+=>X D=+=>Y

G[S]:SbAb A(B|a BAa):

LASTFIRST

SbA(Ba)#S>b)>>#

4-5(1) V(2) Sj-1 Si+1

2. 3+5*25*23+5-23+5 G[E]:EE+E|E*E|(E)|i

+*i+>>

G[E]:EE+E|E*E|(E)|ii+i+i*(i+i)

1#i+i+i*(i+i)#2#i+i+i*(i+i)#Ei3#E+i+i*(i+i)#4#E+i+i*(i+i)#5# E+i+i*(i+i)#Ei6# E+E+i*(i+i)#EE+E7# E+i*(i+i)#8#E+i*(i+i)#9# E+i*(i+i)#Ei10# E+E*(i+i)#

+*i+>>

G[E]:EE+E|E*E|(E)|i

11# E+E*(i+i)#12# E+E*(i+i)#13# E+E*(i+i)#Ei14# E+E*(E+i)#15# E+E*(E+i)#16# E+E*(E+i)#Ei17# E+E*(E+E)#EE+E18# E+E*(E)#19# E+E*(E)#E(E)20# E+E*E#EE*E21# E+E#EE+E22# E#

4-6ab ab > ,< /

P4-7 GABCABCVn,OG

1 2aPaVt,PVnaP 3PaaVt,PaP 4

(1) if then| else if then | else

(2):=|:=|||:=:=

4-8 Ga,bABCVn1.ab GabaBb2.abB=+=>Cb3.a>b GBb,B=+=>aB=+=>aC Ga.b ab abG

G[E]EE+T|T TT*F|F FPF|P P(E)|iVt={+*i}EE+TT=+=>T*F+PF*E+T+>+FPFF=+=>PFE+T=>T+T=>T*F+T=>F*F+T=>PF*F+T=>iF*F+T=>iF*F+T=>iF*F+T*F=>iF*F+F=>iF*F+T*i

4-9FIRSTVT(B)={a|B=+=>aB=+=>Ca}LASTVT(B)={a|B=+=>aB=+=>aC}AabAaBbababAaBFIRSTVT(B)bab

G[E]:EE+T|T TT*F|F F(E)|iFIRSTVTLASTVT FIRSTVT(E)={+,*,(,i} FIRSTVT(T)={*,(,i} FIRSTVT(F)={(,i} LASTVT(E)={+,*,),i} LASTVT(T)={*,),i} LASTVT(F)={),i}

+*i+>>

##N1a1N2a2NnanNn+1#aiNjNjajNiaiNi+1,aj-1ai+1

G[E]EE+T|T TT*F|F F(E)|iT+F##TT+FT

4-10 G[E]EE+T|T TT*F|F F(E)|iT+T*F+iT+T*F+iT+T*FTT*FiT*FiT*F

i+(i+i)*i

1#i+(i+i)*i##+iF2#F+(i+i)*i##

E+TT+TE+FT+FF+FEPQN

4.2.2 LR ,,LRK

LRK1956KnuthLRKKK1LLKLRLRLR

LR(1) LR(2) LRatction,goto(3) LR0)LR

ACTION[Si,aSia4 l: Sj=GOTO[Siaaij 2: AAr||=rr,SPrASj=GOTO[SiA]Sj 3acc: S

4 LRLR G[S](1) SA(2) SB(3) AaAb(4) Ac(5) BaBb(6) Bd

(1) SA (2) SB (3) AaAb (4) Ac (5) BaBb (6) Bd

ACTIONGOTOabcd#SAB0S4S5S61231acc2r1r1r1r1r13r2r2r2r2r24S4S5S6785r4r4r4r4r46r6r6r6r6r67S98S109r3r3r3r3r310r5r5r5r5r5

aaaadbbbb

ACTIONGOTO10#aaaadbbbbS4204#aaaadbbbbS43044#aaaadbbbbS440444#aaaadbbbbS4504444#aaaadbbbbS66044446#aaaadbbbbr687044448#aaaaBbbbbS10804444810#aaaaBbbbbr58904448#aaaBbbbS10100444810#aaaBbbbr58110448#aaBbbS1012044810#aaBbbr5813048#aBbS101404810#aBb#r531503#B#r211601#S#acc

,4-11,S=r=>A=r=> GSSS,SSS

S =r=>A=r=>aAb=r=>a2Ab2=r=> anAbn=r=> ancbn S =r=>B=r=>aBb=r=>a2Bb2=r=> anBbn=r=> andbn a,a2,a3an, anc, and, anA, anB, anAb, anBb, an-1A, an-1B, an-1Ab, an-1Bb,AB (1) SA (2) SB (3) AaAb (4) Ac (5) BaBb (6) Bd

4.2.3 LR(0) LRkLR0LR0LR04.12 AAGLR0

G[E]EE+T|T TT*F|F F(E)|i EE+T EE+T EE+T EE+T ET F(E) FiA||+1AA

SSSSSS#

4.13 AXGLR0XVnVt,LR0AXVnVt*4.14 LR0LR04.15 GLR(0),1.GLR(0) LR(0)NFANFADFA

LR(0)NFA(1) LR(0)NFALR(0)(2) LR(0)NFA(3) ji,ijX(4) iXAiA

:G[A] AaA AbG:G[S]: (0) SA (1) AaA (2) Ab G[S]LR(0)S AAaAAaAAb AbS AAaA

,:

aAb{1,2,4} {3,2,4}{6}{5}{3,2,4} {3,2,4}{7}{5}{6} {5} {7}

,:GDFA,LR(0)

2.GLR(0) ICLOSUREI(1) ICLOSUREI(2) ABCLOSUREIBBBCLOSUREI(3) 2CLOSUREI 4-16 GOIiX=IjIi XX VnVt Ij=CLOSUREAX| AX Ii

G[E]EE+T|T TT*F|F F(E)|iSECLOSURESE={ SEEE+TETTT*FTFF(E)Fi}GLR01I0= CLOSURESSGSSS2IiG Ii Ij=GO(Ii,X)G32

G[S]SS SA SB AaAb Ac BaBb BdLR0I0= CLOSURESS={ SSSASBAaAb AcBaBb Bd}I1= CLOSURESS={ SS}I2= CLOSURESA={ SA}I3= CLOSURESB={ SB}I4= CLOSUREAaAbBaBb={ AaAb BaBb AaAb Ac BaBb Bd }I5= CLOSUREAc={ Ac}I6= CLOSUREBd={ Bd}I7= CLOSUREAaAb={ AaAb}I8= CLOSUREBaBb={ BaBb}I9= CLOSUREAaAb={ AaAb}I10= CLOSUREBaBb={ BaBb}

4-17 S=r=>A=r=>12A121AXAXXBaBbaB, aaB, aaaB, aaaaB,anB

AAAA122AaAb AaAb Ac BaBb BdaaABABSS

//LR:LR,SAc AbAb|bLR,SAc AAbb|bLR, 4-18 LR0//LR0

LR0 LR0G(1) I0I1,In01,n SS(2) Ik a)AaACTION[k.a]Sj,Ij=GO(Iia) b)AaVt{#}ACTION[k,a]=rj,jj c)ABGOTO[k,B]jBIj=GOIk,B d)SSACTION[k,#]acc(3) (4) LR0

S(L)|a LL,S|S LR00SS 1S(L) 2Sa 3LL,S 4LSI0= CLOSURESS={ SSSLSa}I1= CLOSURESS={ SS}I2= CLOSURESL={ SL LL,SLSSLSa }I3= CLOSURESa={ Sa}I4= CLOSURESLLL,S={ LL,S SL}I5= CLOSURELS={ LS}I6= CLOSURELL,S={ LL, SSLSa }I7= CLOSURESL={SL}I8= CLOSURELL, S={ LL, S }

:GO(I0,S)=I1 GO(I0,()=I2 GO(I0,a)=I3 GO(I2L)=I4 GO(I2,S)=I5 GO(I2,()=I2 GO(I3,a)=I3 GO(I4,)=I6 GO(I4,)=I7 GO(I6,()=I2 GO(I6,a)=I3 GO(I6,S)=I8

ACTIONGOTOa#SL0S3S211acc2S3S2543r2r2r2r2r24S7S65r4r4r4r4r46S3S287r1r1r1r1r18r3r3r3r3r3

4.2.4 SLR(1) LR0LR0AFOLLOWALR1SLR1AkSLRk

LR0II={Xb,A,B}SLR1Ia (1) a=b (2) aFOLLOW(A), A(3) aFOLLOW(B), B(4)

LR0ImA11a11, A22a22,Ammamm;nB1B2 Bn,{a1,a2,,am},FOLLOW(B1), FOLLOW(B2),FOLLOW(Bn)an+1

G(1) I0I1,In01,n SS(2) Ik a) Aa ACTION[k.a]Sj,Ij=GO(Ika) b)AaFOLLOW(A)ACTION[k,a]=rj,jj c)ABGOTO[k,B]jBIj=GOIk,B d) SSACTION[k,#]acc(3) (4) SLR1

G[S] 0SE 1EE+T 2ET 3TT*F 4TF 5F(E) 6FiSLRLR0I0=CLOSURESE={ SEEE+TETTT*FTFF(E)Fi}I1=CLOSURESE={ SE EE+T }I2= CLOSUREETTT*F={ ETTT*F}I3= CLOSURETF={ TF}I4= CLOSUREF(E)={ F(E)EE+TETTT*FTFF(E)Fi}I5= CLOSUREFi={ Fi}I6= CLOSUREEE+T={ EE+TTT*FTFF(E)Fi }

I7= CLOSURETT*F={ TT*FF(E)Fi }I8= CLOSUREF(E)EE+T={ F(E)EE+T}I9= CLOSUREEE+T TT *F ={EE+T TT *F }I10= CLOSURETT*F={ TT*F}I11= CLOSUREF(E)={ F(E)} :GO(I0,E)=I1 GO(I0,T)=I2 GO(I0,F)=I3 GO(I0,)=I4 GO(I0,i)=I5 GO(I1,+)=I6 GO(I2,*)=I7GO(I4,E)=I8 GO(I4,T)=I2 GO(I4,F)=I3 GO(I4,)=I4 GO(I4,i)=I5 GO(I6,T)=I9 GO(I6,F)=I3 GO(I6,)=I4 GO(I6,i)=I5 GO(I8,)=I11 GO(I8,+)=I6 GO(I9,*)=I7

FOLLOWS={#}FOLLOWE={+)#}FOLLOWT={+*)#}FOLLOWF={+*)#}

SLR1

ACTIONGOTO+*i#ETF0S4S51231S6acc2r2S7r2r23r4r4r4r44S4S58235r6r6r6r66S4S5937S4S5108S6S119r1S7r1r110r3r3r3r311r5r5r5r5

LR(1) SLRIkAKaFOLLOW(A)AA Aa(Aa ) SLR{a1,a2,,am}FOLLOWASLR

G[S]SL=R SR L*R Li RLLR0I0= CLOSURESS={ SSSL=RSRL*RLiRL}I1= CLOSURESS={ SS}I2= CLOSURESL=RRL={ SL=RRL }I3= CLOSURESR={ SR}I4= CLOSUREL*R={ L*R RL L*RLi }I5= CLOSURELi={ Li}I6= CLOSURESL=R={ SL=RRL L*RLi }I7= CLOSUREL*R={ L*R}I8= CLOSURERL={ RL }I9= CLOSURESL=R={ SL=R}

I2FOLLOWR={#=}{=}SLR2=R=L=RL

ALRAk[Aa1a2a3ak]ALR0a#LRka1a2a3ak[Aa1a2a3ak][ABa1a2a3ak]a1a2a3ak[Aa1a2a3ak]ka1a2a3akAk=1

LR1[Aa]S=r*=>A=r=>1= 2aa#[TT*F+][TT*F*]E+TE+TLR(1) LR1LR0LR1LR0LR1CLOSUREGO

LR1LR11ICLOSUREI2[ABa]CLOSUREIBFIRSTab,[Bb]CLOSUREI32CLOSUREI[ABa]=S=r*=>Aa=r=>BaabBS=r*=>B b=r=>b[Bb]bFIRSTa

LR14-19 LR1GOGOIi,X=IjXXVtVnIiIj=CLOSURE[AXa]| [AXa] IiaVt{#}IiIj= GOIi,XX

GLR1 (1) I0= CLOSURE[SS#]GSSS (2) IiG Ii Ij= GO(Ii ,X)G (3) 2

0S S (1)SBB (2)BaB (3)Bb LR1I0=CLOSURE[S S#]={[S S#][SBB#][BaB,a/b],[Bb,a/b]}I1=CLOSURE[S S#]={[S S#]}I2=CLOSURE[SBB#]={[SBB#],[BaB,#],[Bb,#]}I3=CLOSURE[BaBa/b]={[BaBa/b], [BaB,a/b],[Bb,a/b]}I4=CLOSURE[Bb,a/b]={ [Bb,a/b]}I5=CLOSURE[SBB#]={[SBB#]}I6=CLOSURE[BaB#]={[SaB#], [BaB,#],[Bb,#]}I7=CLOSURE[Bb,#]={ [Bb,#]}I8=CLOSURE[BaBa/b]={[SaBa/b]}I9=CLOSURE[BaB#]={[SaB#]}

LR1 LR1GOLR0SLR1G(1) I0I1,In01n,[SS#](2) Ik a) [Aab]ACTION[k.a]Sj,Ij=GO(Iia) b) [A,b]ACTION[k,b]=rj,jj c) [ABb]GOTO[k,B]jBIj=GOIk,B d)[SS,#]ACTION[k,#]acc(3) (4) LR1

LR1G[S]SL=R SR L*R Li RLLR1G[S](0)SS (1)SL=R (2)SR (3)L*R (4)Li (5)RLLR1I0=CLOSURE[S S#]={[S S#][SL=R#][SR,#], [L*R,=/#][Li,=/#],[RL,#] }I1=CLOSURE[S S#]={[S S#]}I2= CLOSURE[SL=R#],[RL,#]={[SL=R#],[RL,#]}I3= CLOSURE[SR,#]={ [SR,#]}I4= CLOSURE[L*R,=/#]={ [L*R ,=/#][RL,=/#] [L*R,=/#][Li,=/#] }

I5= CLOSURE[Li,=/#]={[ Li,=/#]}I6= CLOSURE[SL=R,#]={[SL=R,#][RL,#] [L*R,#][Li ,#]}I7= CLOSURE[L*R,= /#]={[ L*R,=/#]}I8= CLOSURE[RL,=/#]={ [RL,=/#] }I9= CLOSURE[SL=R,#]={[SL=R,#]}I10= CLOSURE[RL,#]={ [RL,#] }I11= CLOSURE[L*R,#]={ [L*R ,#][RL,#] [L*R,#][Li,#] }I12= CLOSURE[Li,#]={[ Li,#]}I13= CLOSURE[L*R,#]={[ L*R,#]}

ACTIONGOTO*i=#SLR0S4S51231acc2S63r24S4S5875r4r46S11S121097r3r38r5r59r110r511S11S12101312r413r3

LALR(1) LR1SLRSLRSLRLRLALRlook a head-LRLRSLRLR0LR1SLRSLRLALRLR(1)

0S S (1)SBB (2)BaB (3)Bb LR1I0=CLOSURE[S S#]={[S S#][SBB#][BaB,a/b],[Bb,a/b]}I1=CLOSURE[S S#]={[S S#]}I2=CLOSURE[SBB#]={[SBB#],[BaB,#],[Bb,#]}I3=CLOSURE[BaBa/b]={[BaBa/b], [BaB,a/b],[Bb,a/b]}I4=CLOSURE[Bb,a/b]={ [Bb,a/b]}I5=CLOSURE[SBB#]={[SBB#]}I6=CLOSURE[BaB#]={[SaB#], [BaB,#],[Bb,#]}I7=CLOSURE[Bb,#]={ [Bb,#]}I8=CLOSURE[BaBa/b]={[SaBa/b]}I9=CLOSURE[BaB#]={[SaB#]}

I3I6I4I7I8I9a*b a*bI3bBaBba/bI6BbB#a*ba*b a*b a*bI3I6{[SaBa/b/#], [BaB, a/b/#],[Bb, a/b/#]}I4I7{ [Bb,a/b/#]}a*bBa*b a*b a*bbBa*bBSBS a*bS#

4-20 LR1 GOIXILR1GOIXLR1////LALR

LALR(1)GLR1C={ I0I1,In} C={ J0J1,Jm}[SS#]Jk(2)CACTION a) [Aab]ACTION[k.a]Sj,Jj=GO(Jka) b) [A,b]ACTION[k,b]=rj,jj c) [SS,#]ACTION[k,#]acc(3) GOTO JkIi1, Ii2, Ii3,IitIiGOIi1,X, GO(Ii2,X),GO(Ii3,X),GO(Iit,X)Jj,GOJkX= JjGOJkA=Jj,GOTO[k,A]=j,AVn(4)

GLALRG[S](0)SS (1)SL=R (2)SR (3)L*R (4)Li (5)RLLR1I0=CLOSURE[S S#]={[S S#][SL=R#][SR,#], [L*R,=][Li,=],[RL,#] }I1=CLOSURE[S S#]={[S S#]}I2= CLOSURE[SL=R#],[RL,#]={[SL=R#],[RL,#]}I3= CLOSURE[SR,#]={ [SR,#]}I4= CLOSURE[L*R,=]={ [L*R ,=][RL,=] [L*R,=][Li,=] }I5= CLOSURE[Li,=]={[ Li,=]}I6= CLOSURE[SL=R,#]={[SL=R,#][RL,#] [L*R,#][Li ,#]}I7= CLOSURE[L*R,=]={[ L*R,=]}

I8= CLOSURE[RL,=]={ [RL,=] }I9= CLOSURE[SL=R,#]={[SL=R,#]}I10= CLOSURE[RL,#]={ [RL,#] }I11= CLOSURE[L*R,#]={ [L*R ,#][RL,#] [L*R,#][Li,#] }I12= CLOSURE[Li,#]={[ Li,#]}I13= CLOSURE[L*R,#]={[ L*R,#]}J0=I0J1=I1J2=I2J3=I3J4=I411J5=I512J6=I6J7=I713J8=I810J9=I9GO

GOGOJ0S=J1GOJ0L=J2GOJ0R=J3GOJ0*=J4GOJ0i=J5GOJ2==J6GOJ4R=J7GOJ4L=J8GOJ4*=J4GOJ4i=J5GOJ5R=J9GOJ6L=J8GOJ6*=J4GOJ6i=J5

ACTIONGOTO*i=#SLR0S4S51231acc2S6r53r24S4S5875r4r46S4S5897r3r38r5r59r1

LALR GLR1LALR1LR1LR0LR0LALR4-21 SS LR0 A.=)=[B.Cb],C=*r=>A,aFIRST(b),C=*r=>AA

[A.ab][A.Bb]B=*r=>a,aGOTOGOIX=J,IKJL[A.X, a]K,[AX.,a]L,[A.B, a]K, CXK B=*r=>CbFIRST(a),CX,[CX.,b]L LR0LALR1 IGOIX

A.BLR0IK B=*r=>CCXLR1[A.X, a]KGOIX[CX.,b]Lba b B=*r=>CbFIRST(a), bab ba,aa

:IK,@for(K[B.,@]) { J=closure([B.,@]); if([A.X,a] Ja@) GO(I,X)[AX . ,a] ; if([A.X,a] Ja=@) GO(I,X)[AX . ,a] ; IB.GO(I,X) AX . }

LALR(1):(1) GLR(0)(2) for(LR(0)) for(X) GO(I,X);(3)LR(0);(4) [A.X,a]LCX.,aCX.,a(5)(4)

GLALRG[S](0)SS (1)SL=R (2)SR (3)L*R (4)Li (5)RLI0: S.S,@ S.L=R,@ S.R ,@ L.*R,=/@ L.i=/@ R.L ,@ I1: SS.,@ I2: SL.=R,@ RL. ,@ I3: SR. ,@ I4: L*.R,@ R.L ,@ L.*R ,@ L.i ,@ I5: Li.,@ I6: SL=.R,@ R.L ,@ L.*R ,@ L.i ,@ I7: L*R.,@ I8: RL. ,@ I9: SL=R.,@

:(I0: S.S , I1: SS. )(I0: S.S , I2: SL.=R)(I0: S.S , I3: SR. )(I0: S.S , I4: L*.R)(I0: S.S , I5: Li.)(I2: SL.=R ,I6: SL=.R) (I4: L*.R , I4: L*.R)(I4: L*.R , I5: Li.)(I4: L*.R , I7: L*R.)(I4: L*.R , I8: RL. )(I6: SL=.R, I4: L*.R) (I6: SL=.R, I5: Li.)(I6: SL=.R, I8: RL. ) (I6: SL=.R, I9 :SL=R.)

I0: S.S##I1: SS.#I2: SL.=R #I3: SR. #I4: L*.R ==/#I5: L.i ==/#I6: SL=.R#I7: L*R.=/# I8: RL.=/# I9: SL=R.#

GOGOI0S=I1GOI0L=I2GOI0R=I3GOI0*=I4GOI0i=I5GOI2==I6GOI4R=I7GOI4L=I8GOI4*=I4GOI4i=I5GOI5R=I9GOI6L=I8GOI6*=I4GOI6i=I5LALR

4.2.6 LRSLRLALRLRG[E]:EE+E|E*E|(E)|iG[E]:EE+T|T TT*F|F F (E)|i ,LR

G[E]:EE+E|E*E|(E)|iLR0I0=CLOSURESE={ SEEE+EEE*EE(E)Ei}I1=CLOSURESE={ SE EE+T EE*T }I2=CLOSUREE(E)={E(E)EE+EEE*EE(E)Ei }I3= CLOSUREFi={ Fi}I4= CLOSUREEE+E={ EE+EEE+EEE*EE(E)Ei }I5= CLOSUREEE*E={ EE*EEE+EEE*EE(E)Ei }

I6= CLOSUREE(E)EE+EEE*E={ E(E)EE+EEE*E }I7= CLOSUREEE+EEE+EEE*E={ EE+EEE+EEE*E }I8= CLOSUREEE*EEE+EEE*E={ EE*EEE+EEE*E }I9= CLOSUREE(E)={ E(E)} FOLLOWS={#}FOLLOWE={+*#}

I7EE+EEE+EEE*EEE+EFOLLOWE={+*#}EE+EEE*E{+*}SLRLR1LR1E+E++E+E**I8

ACTIONGOTO+*i#E0S2S311S4S5acc2S2S363r4r4r4r44S2S35S2S36S4S5S97r1S5r1r18r2r2r2r29r3r3r3r3

SSSiSeS|iS|a:I0=CLOSURESS={ SSSiSeSSiSSa}I1=CLOSURESE={ SS}I2=CLOSURESiSeSSiS={ SiSeSSiS SiSeSSiSSa }I3=CLOSURESa={ Sa}I4=CLOSURESiSeSSi S={ SiSeSSi S }I5=CLOSURESiSeS={ SiSeS SiSeSSiSSa }I6=CLOSURESiSeS={ SiSeS}I4SiSeSSi Sfollow(s)e,SLR

ACTIONGOTOiea#S0S2S311acc2S2S343r3r34S5r25S2S366r1r1

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