Complexity of Context-free Grammars with Exceptions, and the inadequacy of grammars as models for XML and SGML
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(199) 2(N 1:Wm*-N6 N61N U{HM&WmN6 b`:1 W"N U{2:N :1Wm*-N6 H7Q^`:1: W(/N U M)+ HMjkW')K 1HMmj95 & '( !*K 56i2NX 1Wm*-N6 H<MNc5 & '( !Men 'g/)+ HM%W')+ 1HM Ba !UQM' )K)4e2'nX*-N61H W')+ 1H&HI xn ? )+& g8`a'& t5 & '( !M& $1H(*+ 5p2(N 1:Wm*-N6 HZN61IN U;/[:(HM
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(201) 'vO' *+ O2N 2aN6HM& Z '(*+nG !*-N6
(202) N6 )-g^*+( U *+H{UQ )+H7QM(1o<=1 : '!ª]l1l&
(203) 2:N 2aN6HM&
(204) '(*+nG !*-N6 'n 'e1HM&H q N6 CM'(Y
(205) *+ ¬ ) . ;7 ik<"B& Wmq N/WmN6J W:*+Wm vO*+p z*+Y
(206) 2N6H& \msXWm'2*+N6 zNXW'W'1(H )-N6 5Z 2N 2aN6HM& } '"*-nG !*+N6 ] §;©êu%HH1Y
(207) i'ms*+HMHZ p '"*-nG !*+N6 N & U R *+ · l:]tN6)+)-Nxv´*+H '(*+nG !*-N6 8UQN6Y )+'UVZMN (*-56C'BaW')+ 1HMe !UVM';W')+ 1H ]O $& ?(1)- jíÏÎ 97 232U i9 < jÔ/> . nVF=*KH&YZ2:)+Nxg & Ba& ? '[:  °¯²± ]= $&
(208) "1)-0 ªl;7 >9< ® jÎÏ 97 %"% n9< "j /> . iVF*+Hl&YZ2:)+Nxg & BC&
(209) '[: # ªl;7 >§< Â ªD³µ´9¶· ] %Wm )-N 5 N61H)+gbvO& 'n ';N '/MW')+ 1:HMmj95 & '( !*+ 56}(1)-&H%UQN6Y Z["HM`:1 W"? !(Z& WmN61 Xj M'& i i )+HMNv& q ?M)+ HMjkW')+ 1:HMmj95 & '( !*+ 56^"1)-O*+H'n & L1: )+)-gZ&YZ2:)+Nxg & ]lP
(210) %& BCvO& & W(W')+ 1HMc He`a'& 5 & '( !M& BWmN6Y
(211) 2:)-'Mc} '[: *+*-N6 pN U% HH*-56 Y
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(213) *K WmN6 H*+HM& Wmgq*+ i '[f *-*-N6 IN 1 U ª?W' xn
(214) NW'W'1& ]Z.N ('Nxn '&B<ªr*+H; cM(1 HH(*-56 YZ& CvO*+W"Y
(215) !0 &H !)-& H;N6
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(217) ?)K 561 !5 ß ¢ uÉ vO& r' ms*+HM Z2aN6)-gX N6Y
(218) *+ )¹ 7°k¤<"Bf U Y
(219) *+)-g/õxÍ l Ù p} Ò P ÷ N Ul )-5 N (*+Y
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(221) N6HM< 7;<"ú ø )-& 5 }N U &HWm(*-2*+N6 IN UlÍ#lI*+HO !OYZN6HM8 7;<"]. *.
(222) WmN6YqYZN6 q`a&)+*+'Ul7*K b>d&GF9B !2: !5 º* TBHM'%%5 & '( ) *+HW'1:HH*-N6
(223) !`aN61 N6 G³M&Wm1% UQN6)+)-NxvJ%'UQ'& Wm&H56*-n & f<²1*-MW')+N6HMMN Â X %8N6 B*+H: ! %ljkWmN6YZ2f)-'M2N `:)-&YqHW' N `a;HMN6)-n & b N6 Xjk1 :*-UVN "Y
(224) )-g
(225) *+ c2aN6)-gX N6Y
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(228) Y
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(230) *+ !*+ 5}&Y Yq &gzW' 1HImsX2aN6 & L*K ){5 Nov8*+ piH*-,'IN U ^5 ( Y
(231) Y
(232) !&]« UQN 1 : !M&)-g Bf'N &YÔ] I N&H N Wm1 )+)+g &HHO^Y
(233) N *-nG !*+N6 /`a&*+ : /WmN6 !³&Wm1(/N U;° *+)-2a&) ± *K & : t NN >dmF9¡b*-
(234) NC&HI N
(235) 2Non*K [: )E'nX*+ & :Wm !IH(1W( msX2N6 & L*+ )5 NovvN61)+ )+HMN%&H1)+UQN6Y&)+*+Y
(236) *K !*+ 5msWm'2*-N6 :H=UVN6Y# ./3H']=P '& B 'N (&Y] W')-& !()-g*K *+W' !M&H !lmsXM& & ZWmN6 CMmsj9UQ'5 ( Y
(237) Y
(238) !(H=v*-emsXWm'2*+N6 H=²N ?'lN6 :)-g
(239) *+Y
(240) 2'(UV&Wm=Y
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(242) *+)+g}N U msXM& & WmN6 CMmsj9UQ'^5 ( Y
(243) Y
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(245) N6HM=&HM2aN6 H*-`f)- UQN ( Yq !*+W À* ?'& :Wme*+ bWmN6YZ2:)-ms*-hg}`&: &nX*-N &]OP b*+HvE &g BvN 2aMNc*+ C !HMN6YZeN U N6HM HM2a&WmH=vO:*+W(^2aN6HH*-`:)+g%)+*KY
(246) *-4n! )+*+ *+kg ( ÁoN lH1:*- !`:*+)+*+kgN U:5 ( YqY
(247) !(HvO*-^msXWm'2:*-N6 H HO ZY
(248) N &)UVN %:#;./3 }~;./3]. Â. ÃiÄÆÅ. Ç. f#e`g %g lRe8È ÊÉ&`ee´¼OºË¼Ë. º`gÌc`ÍÎe8È^ <e!Ï^%%g. P q*KHHM&Wm*+N6 BXv*+ *KW' !MOvO !E*+ qN61EN 2:*+ *-N6 q !hvNZY
(249) *K q& HN6 HUVN ; *+HWm('2: Wmg `a'kv'& :#;./3i ^*-HmsXM& & ^WmN6 LMmsXj9UV('5 " Y
(250) Y
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(254) N U*+H'n & C^ N 2:2:*+ 5c c !57QMN `aM(1 BX'( !;HMN6YZ;(1)+&HMN
(255) )K)-NxvuHMN6YZ; !5ZN6Yq*+HH*-N6 BC`:1E*K '& B;(1)+&H !³1HM 'HMNZ !OvW' b Wm1 )+)-gc*+ UQ' Y
(256) *KHH*+ 5 !56H"<"ú ø *K u:#;./3BUQN Cgw N6 Xj9M'"Y
(257) *+ )'*+Hi 8H*+ 56)+b2(N 1:Wm*-N6 tvO*+w N6 $?)+'UVj : /H*K ]*+H2N6*K LN U{ *+HM*+ :Wm*-N6 }`a&WmN6YZ&H&)-'n! LvO& msWm'2*-N6 :H% !(0 '21 ' WmN6 :H*+ '( !*+N6 ] R%U&HM&)+&YZ& LHN U :*+HM*+ Wm*+N6 B![(H=WmN6 :Wm'( Hl`aN Z~;./3b I# ./3b Z
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(259) ! 'N ge>d&!F9B &n! *+)+ !`f)- !>dx@oF9]= J:*+)-{v2a'(Wm&*+n & ^ H=Wm(1W'*K )L )+HMN%HM&WmN6 &)-&YZ& CN U :*+HM*+ Wm*+N6 *+ qW' HIN U# ./3Bvi N/ N ^`a&)+*-'n
(260) IH YZqMN?N6)+ zUVN ^~.b3{B H*+ :Wmi~;.b3¬ N&H
(261) N
(262) )+)+Nxv©msWm'2*-N6 H
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(265) !(Hv*-}msWm'2*-N6 H &n e&*-O)K*+Y
(266) *-H*+ YZNX &)+*+ 5c#;.b3{BaZ*+ & H%*K be2:NCN UN U'N (&Y ] cW' \2aN6HH(*-`:)-g}&)-2*+ ?1 '(HM *K 5 vO*KW(e HM2a&WmHN {*K 5 & *-& CHN UfmsXWm'2*+N6 eY
(267) &W( *KHY HN61)+ ^ '[: *+M&)-g; N =`*+ W')+1: & BGUVN 'qW'*-& :Wmg& HMN6 :H'B6*+ CMN%~;./3/HM !( ]E79R%xB6 !=)+& HM'B6vE N% N =0X Nxv_N UfN 'lUQN (Y
(268) )HMM'2:H N 2: !(*+ )a&H1)+HEN6 }*+HEUQN6 C']¤<eP : '& B 1H;N UmsWm'2*-N6 H`'56*K HEMNq !22a& !WmN6 CMNxn '(H(*+ ) 'n & UQN 1N (H&B4*+ ? !'B4 )-N6156\msXWm'2:*-N6 H !
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(270) & *-& B{N i !MM(*-`:1M& 8MNp2aNCN
(271) HMhg)+/*+ 81H}N U msWm'2*-N6 H'B*-i*KHqHNovO $*+ Ó>T!F9BN6 Jb`f H*+H
(272) N U^ w&Y
(273) 2:*-(*+W' ) )-gXH*+H'BE !c\WmN6YZ2:)+msX*-hg N UHMN6YZI%O%He*+H^ !22N6 W"*+ 57QN e H^msXWm'& & <;Y
(274) !5 & !`f)-I)+*KY
(275) *-H56*-n & msX*KHM*+ 5}MNN6)+H^UVN &H*+56 *+ 5
(276) b1 '"HM *+ 5e&Y}Bf b*-O*+HO NxvE &gXHWmN6Y
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