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ERGO ?>:8 I> T T48=>N :><?0=VTN, O:0 <0T ?0@A5@, 740B=89 287=0G0B8 B8? 70?8B0==O (?8B0==O 4> ?V4<5B0, AC1'T:B0, ?@O<>3> 01> =5?@O<>3> 4>40B:0, G8 >1AB028=8) V "<8BBT2>" :>=AB@CN20B8 2V4?>2V4L. 48= 7 =091V;LH 240;8E A8=B0:A8G=8E 0=0;V70B>@V2 Functional Dependency Grammar [] AB2>@5=89 4>A;V4=8:0<8 7 5;LA8=AL:>3> C=V25@A8B5BC, :>B@V ?V7=VH5 70A=C20;8 42V DV@<8: Lingsoft V Conexor. 0==O 25@AVO ?V4 =072>N ENGCG (English Constraint Grammar) 1C;0 28:>@8AB0=0 4;O 0=>B0FVW =091V;LH>3> C A2VBV :>@?CAC  Bank of English, I> =0;568BL 28402=8FB2C Collins/Harper Publishers. A>1;82VABN 40=>3> A8=B0:A8G=>3> 0=0;V70B>@0 T B5, I> C 28?04:0E, :>;8 =5<>6;82> 7=OB8 1030B>7=0G=VABL, A8=B0:A8G=89 0=0;V70B>@ 01> 2840T 45:V;L:0 20@V0=BV2 0=0;V7C, 01> =5 4>1C4>2CT 45@52> 4;O 40=>W G0AB8=8 ?@>?>78FVW. 48= 7 =091V;LH >@83V=0;L=8E ?V4E>4V2 4> A8=B0:A8G=>3> 0=0;V7C B5:ABC  Link Parser []  @>7@>1;5=89 2 Carnegie-Melon University. &59 A8=B0:A8G=89 0=0;V70B>@  T48=89, G8W ?>G0B:>2V :>48 1C;8 >?C1;V:>20=V >=-;09=. 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"5@<V=>;>3VG=5 ?>=OBBO ?@54AB02;5=5 V<5==>N 3@C?>N, C O:V9 V<5==8: <>65 <0B8 70;56=89 5;5<5=B. > 7030;L=>=0C:>2>W ;5:A8:8 (ls2) 2V4=>A8;8AO BV V<5==8:8 (V<5==V 3@C?8) 7 >@83V=0;L=8E B5:ABV2 V B5:ABV2 WE V=48:0B82=8E @5D5@0BV2, O:V <>6CBL 7CAB@VG0B8AO 2 B5:AB0E 1C4L-O:>W ?@54<5B=>W 30;C7V, 0 B0:>6 4VTA;>20 7 =0O2=VABN A5<0=B8G=8E >7=0: m1, m2 V m3. # ?@>F5AV 40=>3> 4>A;V465==O 1C;0 AB2>@5=0 28@>465=0 >=B>;>3VO 7030;L=>=0C:>2>W ;5:A8:8 @>AV9AL:>W <>28, C O:C C2V9H;8 ;5:A5<8 B@L>E :;0AV2 2V4?>2V4=> 4> <5B07=0G5==O (m4, m5, m6) (>40B>: ). 5:A5<8, I> =5 7304CNBLAO 2 A;>2=8:0E  G8 , 22060;8AO ?@8=0;56=8<8 4> 7030;L=>26820=>W ;5:A8:8 (ls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m4, m5, m6, 37%  4VTA;>20<8 7 <5B07=0G5==O<8 m1, m2 V m3, 0 13%  7030;L=>26820=8<8 ?@8:<5B=8:0<8 7 >FV=>G=8< 7=0G5==O<.  >3;O4C =0 B5, I> ?5@5206=0 1V;LHVABL ;5:A5<, C6820=8E C B5:AB0E V=48:0B82=8E @5D5@0BV2, 15@5BLAO 7 B5:ABV2 ?5@H>465@5;, <>6=0 7@>18B8 28A=>2>: ?@> <>6;82VABL AB2>@5==O 0;3>@8B<C 4>1>@C ;5:A5< 7 >@83V=0;L=>3> B5:ABC 2 @5D5@0B82=89. &V:0289 B0:>6 B>9 D0:B, I> 2V4A>B:>289 2<VAB ;5:A8:8  2 B5:AB0E 7 A>FV>=V:8 28I5, =V6 2 V=H8E 30;C7OE, >A:V;L:8 40=0  <VAB8BL C A>1V A>FV>;>3VN, ?A8E>;>3VN, ?>;VB>;>3VN, B>1B> B@8 @V7=8E . >6=0 ?@8?CAB8B8, I> =0C:>2V B5:AB8 2 ?@54<5B=8E 30;C7OE, I> 7=0E>4OBLAO =0 AB8:C 45:V;L:>E 30;C759, 2V4@V7=ONBLAO 1V;LH>N :>=F5=B@0FVTN B5@<V=V2, 0 >B65, ?>1C4>20 02B><0B8G=>3> @5D5@0BC 4;O B0:8E B5:ABV2 ?5@5410G0B8<5 =0O2=VABL >=B>;>3V9 CAVE , =0 AB8:C O:8E 7=0E>48BLAO 40=0. ;O ?>40;LH>W :;0A8DV:0FVW V<5==8E 3@C?, I> 70?>2=NNBL 0:B0=B8 , 7 OAC20;>AO, ;5:A5<8 O:8E A;>2=8:V2 Ls T =>AVO<8 <5B07=0G5=L m4  m9 C @5D5@0B82=><C B5:ABV. >AVO<8 <5B07=0G5==O m4, I> :;0A8DV:CTBLAO 2 >=B>;>3VW 25@E=L>3> @V2=O O: >1'T:B (?V4@>74V; 2.3), <>6CBL 1CB8 7030;L=>=0C:>2V V B5@<V=>;>3VG=V ?>=OBBO, =0?@8:;04: N(m4ls1)  B5@<V=8 7 <5B07=0G5==O< >1'T:B: <>45;L O7K:0, A5<0=B8G5A:0O <>45;L, ;5:A8G5A:>5 7=0G5=85, A8AB5<0 C?@02;5=8O 1070<8 40==KE, O7K: 70?@>A>2, 8=D>@<0F8>==>-?>8A:>20O A8AB5<0, 1070 40==KE; B0@8D=K5 AB02:8, A515AB>8<>ABL, M:>=><8G5A:85 @5D>@<K, B>20@>?@>872>4AB2>, @K=>G=0O ?;0B565A?>A>1=>ABL, M:A?>@B=>5 ?@>872>4AB2>, 8=25AB8F8>==K9 ?>B5=F80;; 0=B@>?><>@D=>ABL, <56;8G=>AB=K5 >B=>H5=8O, A>F80;L=>-?A8E>;>38G5A:85 O2;5=8O, A>F85B0;L=0O ?A8E8:0, 8=D>@<0F8>==K9 <5B01>;87<; @0: ;53:8E, M?845<8>;>38G5A:0O A8BC0F8O, DB8780B@8G5A:0O A;C610, 2>71C48B5;8 701>;520=8O, E8<8>?@5?0@0BK, @5F8482K; N(m4ls2)  7030;L=>=0C:>2V ?>=OBBO 7 <5B07=0G5==O< >1'T:B: 0;3>@8B<, 0A?5:B, 2>?@>A, :>=F5?F8O, <5B>4, <>45;L, >?@545;5=85, ?>;>65=85, ?@87=0:, ?@8=F8?, ?@8G8=0, ?@>1;5<0, ?@>F54C@0, @5:><5=40F8O, A2>9AB2>, A8AB5<0, AB@C:BC@0, B8?. >AVO<8 <5B07=0G5==O m5, I> :;0A8DV:CTBLAO 2 >=B>;>3VW 25@E=L>3> @V2=O O: ?@>F5A (?V4@>74V; 2.3), <>6CBL 1CB8 B0:>6 7030;L=>=0C:>2V V B5@<V=>;>3VG=V ?>=OBBO, =0?@8:;04: N(m5ls1)  B5@<V=8 7 <5B07=0G5==O< ?@>F5A: <548:0<5=B>7=>5 ;5G5=85, :C?8@>20=85, B@0=A?;0=B0F8O; 8=25AB8@>20=85, :@548B>20=85; N(m5ls2)  7030;L=>=0C:>2V ?>=OBBO 7 <5B07=0G5==O< ?@>F5A: 4>AB865=85, 87CG5=85, 8A?>;L7>20=85, 8AA;54>20=85, >1>A=>20=85, >1@01>B:0, >?8A0=85, >@30=870F8O, >ACI5AB2;5=85, ?>AB@>5=85, ?@54AB02;5=85, ?@5>1@07>20=85, @0728B85, @0A?@545;5=85, @0A?@>AB@0=5=85, AB0=40@B870F8O, CA>25@H5=AB2>20=85, D>@<8@>20=85. 5B07=0G5==O m6, m7, m8 C @5D5@0B82=8E B5:AB0E <0NBL BV;L:8 7030;L=>=0C:>2V ?>=OBBO, =0?@8:;04: N(m6ls2)  7030;L=>=0C:>2V ?>=OBBO 7 <5B07=0G5==O< 2;0AB82VABL: 0:BC0;L=>ABL, 045:20B=>ABL, 206=>ABL, =5>1JOA=8<>ABL, ?>?C;O@=>ABL, ?@02><5@=>ABL, MDD5:B82=>ABL; N(m7ls2)  7030;L=>=0C:>2V ?>=OBBO 7 <5B07=0G5==O< <5B0: 4;O >?8A0=8O, 4;O ?>AB@>5=8O, 4;O @0A?@545;5=8O, 4;O C;CGH5=8O; N(m8ls2)  7030;L=>=0C:>2V ?>=OBBO 7 <5B07=0G5==O< 70AV1: <5B>40<8, <>45;O<8, A ?><>ILN; >AVT< <5B07=0G5==O m9 C @5D5@0B82=8E B5:AB0E T 7030;L=>=0C:>20 ;5:A8:0 7V 7=0G5==O< <VAFO ?@>2545==O 4>A;V465==O G8 28:>@8AB0==O 9>3> @57C;LB0BV2, =0?@8:;04: N(m9ls3)  7030;L=>26820=V ?>=OBBO 7 <5B07=0G5==O< <VAF5: 3>@>4, >1;0ABL, @538>=, #:@08=0, 2@>?0, <8@. 0 B@5BL><C  70:;NG=><C 5B0?V :;0A8DV:0FVW V<5==8E 3@C?, I> 15@CBL CG0ABL C 70?>2=5==V 0:B0=BV2 , 2V41C20TBLAO ?>4V; V<5==8:V2 70 3@0<0B8G=>N >7=0:>N G 70;56=> 2V4 BVTW 3@0<0B8G=>W D>@<8, C O:V9 ;5:A5<0 7 40=8<8 >7=0:0<8 M V Ls <>65 26820B8AO 2 ! @5D5@0B82=>3> B5:ABC, 45:  "0: ?>=OBBO 7 <5B07=0G5==O<8: {>1'T:B}, {?@>F5A} V {2;0AB82VABL} <>6CBL 28ABC?0B8 C D>@<V O: =0782=>3>, B0: V 157?@89<5==8:>2>3> @>4>2>3> 2V4<V=:0, B>4V O: ?>=OBBO 7 <5B07=0G5==O< {<5B0} C6820NBLAO BV;L:8 C D>@<V @>4>2>3> 2V4<V=:0 7 ?@89<5==8:><, ?>=OBBO 7 <5B07=0G5==O< {70AV1}  C D>@<V >@C4=>3>, 0 ?>=OBBO 7 <5B07=0G5==O< {<VAF5}  <VAF52>3> 2V4<V=:0. "0:8< G8=><, :;0A8DV:0FVO V<5==8E 3@C? 2V41C20TBLAO 2 B@8 5B0?8 (0;. 3.4). 1. >4V; V<5==8:V2, O:V 2E>4OBL 4> A:;04C V<5==8E 3@C?, I> 70?>2=NNBL 0:B0=B8 @5D5@0B82=8E !, 70 A5<0=B8G=>N >7=0:>N M =0 :;0A8: N(m4), N(m5), N(m6), N(m7), N(m8) G8 N(m9). 2. >4V; 70 >7=0:>N ?@8=0;56=>ABV 4> ;5:A8:8 Ls =0 :;0A8: N(ls1), N(ls2), N(ls3). 3. >4V; 70 3@0<0B8G=>N >7=0:>N G =0 :;0A8: N(G3)=V(g11g71), N(G4)= V(g11g72), N(G5)= V(g11g73), N(G6)= V(g11g74). 8E>48BL, ;5:A8:>-A5<0=B8G=8<8 >7=0:0<8 @5D5@0BC R T:  >45;;N C7030;L=5==O =0 ;5:A8:>-A5<0=B8G=><C @V2=V T 287=0G5=89 =01V@ <5B07=0G5=L ;5:A5<, I> 70?>2=NNBL 0:B0=B8 @5D5@0B82=8E :>=AB@C:FV9, >?8AC20=8E 70 4>?><>3>N >=B>;>3VW 25@E=L>3> @V2=O (A;>2=8: :0B53>@V9). 3.4.3. 0?>2=5==O 0:B0=B=>W AB@C:BC@8 @5D5@0B82=>W :>=AB@C:FVW. 0?>2=5==O 0:B0=B=>W AB@C:BC@8 !> @5D5@0B82=>3> B5:ABC ?>G8=0TBLAO 7 70?>2=5==O V<5==>3> 0:B0=B0 A1 =09G0ABVH5 C6820=8< ?>=OBBO< N1 7 B5:ABC >@83V=0;C, I> 287=0G0TBLAO AB0B8AB8G=8< <5B>4><. 1'T:B G8 ?@>F5A, >?8A0=89 B5@<V=>;>3VG=8< ?>=OBBO<, <>65 1CB8 A0<>ABV9=8< >1'T:B>< 4>A;V465==O 2 B5:ABV ?5@H>465@5;0, 0 7=0G8BL 28ABC?0B8 2 @>;V A1 2 0:B0=B=V9 AB@C:BC@V V=48:0B82=>3> @5D5@0BC. # ?5@5206=V9 1V;LH>ABV 28?04:V2 N1  EMBED Equation.3  N(m4ls1), =0?@8:;04:  A<KA; ?5G5=L B5:AB @538>= B@0=A?>@B ?A8E8:0 0=89 0:B0=B :;0A8DV:CTBLAO O: >1'T:B. >=OBBO, O:5 2V4=>A8BLAO 4> :0B53>@VW >1'T:B, 2 >=B>;>3VW 25@E=L>3> @V2=O E0@0:B5@87CTBLAO O: A0<>ABV9=5 <0B5@V0;L=5 ?>ABV9=5 @5?@575=BCNG8 @50;L=VABL ?>=OBBO. /:I> ?@8:<5B=8: Adj AC?@>2>46CT O4@> A;>2>A?>;CG5==O (V<5==8:) N1 C 1V;LH>ABV 28?04:V2 9>3> 26820==O 2 >@83V=0;L=><C B5:ABV, B> A1=Adj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quation.3  N(m4ls1), B> A2=N2, =0?@8:;04: A>F85B0;L=0O ?A8E8:0 =5A;CG09=>9 3@C??K 8=B53@0;L=K9 B8? !( 65;57=>4>@>6=K9 B@0=A?>@B #:@08=K 0;V @>73;O40TBLAO ;V2>AB>@>==T ?>=OBBO, @>7B0H>20=5 :>=B0:B=> 7 :;NG>28< ?>=OBBO< C B5:ABV >@83V=0;C. N3  EMBED Equation.3  N(m4ls1) v N(m4ls2) v N(m5ls1) v N(m5ls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quation.3  N(m4ls2) v N(m5ls2), B>: A1= N4 A2= N3 A3= N1 A4= N2 , =0?@8:;04: =5>1E>48<>ABL <0B5<0B8G5A:>3> >?8A0=8O A<KA;0 0A?5:BK B@0=A?;0=B0F88 ?5G5=8 ?@>1;5<0 ?>=8<0=8O B5:AB0 >F5=:0 8=25AB8F8>==>9 ?@82;5:0B5;L=>AB8 @538>=0 C;CGH5=85 ?>;>65=8O 65;57=>4>@>6=>3> B@0=A?>@B0 #:@08=K 0?>2=5==O 0:B0=BV2 Ai @5D5@0B82=>W :>=AB@C:FVW 2V41C20TBLAO 4>B8, ?>:8 2 0:B0=B=V9 AB@C:BC@V @5G5=L >@83V=0;L=>3> B5:ABC 28O2;ONBLAO ?>=OBBO Ni, 45 N3  EMBED Equation.3  N(m4ls2) v N(m5ls2). :B0=B Ai 70?>2=NTBLAO 5;5<5=B0<8 !< V !7 7V 7=0G5==O<8 <5B0 V 70AV1, 2V4?>2V4=>, C 28?04:C WE D>@<0;L=>3> @>7?V7=020==O 2 B5:ABV >@83V=0;C (?V4@>74V; 3.3), O:I> 2 !< 3>;>2=89 5;5<5=B Ni  EMBED Equation.3  N(m7ls2g11g72), 0 2 !7 3>;>2=89 5;5<5=B Ni  EMBED Equation.3  N(m8ls2g11g73). :B0=B=0 AB@C:BC@0 :>=AB@C:FV9 !@ 2V4@V7=OTBLAO 2V4 !> =0O2=VABN 7030;L=>=0C:>2>3> ?>=OBBO 7V 7=0G5==O< (m6ls2)  2;0AB82VABL (>FV=:0). @8 ?>1C4>2V :>=AB@C:FV9 !@ ?>G0B:>289 5B0? 70?>2=5==O 0:B0=B0 A1 2V41C20TBLAO 70 BVTN 6 AE5<>N, I> 9 ?@8 ?>1C4>2V !>. 4=0: 70 =0O2=>ABV 2 0:B0=B=V9 AB@C:BC@V @5G5=L >@83V=0;L=>3> B5:ABC ?>=OBL 7V 7=0G5==O< (m6ls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i. /:I> 2 @5G5==V, I> <VAB8BL ?>=OBBO N1 C B5:ABV >@83V=0;C, DC=:FVN ?@548:0B0 28:>=CT 4VTA;>2> 7 3@0<0B8G=>N >7=0:>N (g13g21g31g43g51) V A5<0=B8G=>N >7=0:>N (m1 v m2 v m3,) (@0AA<>B@8<, ?@>0=0;878@C5<, A@02=8<), B> ?@548:0B=89 0:B0=B @5D5@0B82=>W ! 70?>2=NTBLAO BVTN 6 ;5:A5<>N, 0;5 C D>@<V (g14g21g32g42g82 v g13g22g32g41) (@0AA<0B@8205BAO - @0AA<>B@5=, 0=0;878@C5BAO - ?@>0=0;878@>20=, A@02=8205BAO). 4=0: 70 2V4ACB=>ABV 2 B5:ABV >@83V=0;C B0:8E ;5:A5< ?@548:0B=89 0:B0=B 70?>2=NTBLAO ;5:A5<>N 7 :;0AC V(m1), V(m2) G8 V(m3) 70;56=> 2V4 A5<0=B8G=>3> 7=0G5==O S @5G5==O !. "0: ?@548:0B=5 O4@> @5G5=L !> A;C3CT 28=OB:>2> 4;O A8=B0:A8G=>W >@30=V70FVW @5G5==O V 28@065=> ?@548:0B>< V(m1), =0?@8:;04: 0=> A>2@5<5==>5 >?@545;5=85 =5AB018;L=>9 AB5=>:0@488. 7;>65=0 ?@>1;5<0 >1>A=>20=8O 8 <>45;8@>20=8O A>F85B0;L=>9 ?A8E8:8 =5A;CG09=KE 3@C??. ?8AK205BAO AB@C:BC@0 O7K:0 70?@>A>2 4;O A8AB5<K C?@02;5=8O 107>9 40==KE. 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F5=5=K 0:BC0;L=>ABL 8 7=0G8<>ABL 40;L=59H59 ?5@A?5:B82K B@0=A?;0=B0F88 ?5G5=8. # B><C 28?04:C, :>;8 ?@548:0B=5 O4@> T =>AVT< A5<0=B8:8 02B>@AL:>W >FV=:8, 2>=> 28@065=5 V(m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A:V;L:8 =0 2E>4V FL>3> 5B0?C 265 T 3>B>289 0:B0=B=89 ;0=FN6>:, O:89 <VAB8BL >A=>2=89 7<VAB >AB0B>G=>3> @5G5==O 4;O @5D5@0B82=>3> B5:ABC, 3>;>2=8< 70240==O< FL>3> 5B0?C T 281V@ ?@548:0B=>3> O4@0 7V A;>2=8:0 V(m1) (?V4@>74V; 3.4.1). 81V@ ?@548:0BC 7 ?5@H>W 3@C?8, B>1B> 7V A;>2=8:0 V(m1) <>6;82> @>18B8 2 02B><0B8G=><C @568<V, >A:V;L:8 5;5<5=B8 FL>3> :;0AC T ?>2=VABN 270T<>70<V==8<8 (?V4@>74V;V 3.4.1.), :@V< B>3>, =0O2=VABL 2V4V1@0=>3> ?@548:0BC 2 B5:ABV >@83V=0;C =5 >1>2 O7:>20. @8 >D>@<;5=V >AB0B>G=>3> 20@V0=BC  70 4>?><>3>N ?@548:0B0 7 4@C3>W B0 B@5BL>W 3@C? 4VT 7>2AV< V=H89 <5E0=V7<, B><C I> 2 FL><C 28?04:C =5>1EV4=>, ?>-?5@H5, 7=09B8 =5>1EV4=5 A;>2> 2 ?5@28==><C B5:ABV, ?>-4@C35, ?@>0=0;V7C20B8 9>3> >B>G5==O 4;O 287=0G5==O @V2=O C7030;L=5==O V BV;L:8 B>4V 28:>@8AB>2C20B8 9>3> 4;O ?>1C4>28 . ;O ?5@52V@:8 70?@>?>=>20=>3> 0;3>@8B<C 02B><0B8G=>3> @5D5@C20==O 1C;0 AB2>@5=0 5:A?5@8<5=B0;L=0 A8AB5<0  2B> 5D5@0B . @>3@0<=0 G0AB8=0 @>7@>1;5=0 ?@>3@0<VAB>< ..>20;L>28< =0 107V 0FV>=0;L=>3> B5E=VG=>3> C=V25@A8B5BC  %0@:V2AL:89 ?>;VB5E=VG=89 C=V25@A8B5B . @>3@0<=0 @50;V70FVO 74V9A=N20;0AL =0 <>2V !++, A5@54>28I5 @>7@>1:8  Borland C++ Builder 6.  2B>@5D5@0B ?@0FNT GVB:> 70 70?@>?>=>20=8< 0;3>@8B<><. 0 ?5@H><C 5B0?V 2V4HC:CTBLAO =09G0ABVH5 C6820=5 ?>=OBBO H;OE>< 7VAB02;5==O A;V2, O:V 2E>4OBL 4> A:;04C 703>;>2:C, V A;V2 >@83V=0;L=>3> B5:ABC. 024O:8 <5E0=V7<0< <>2 ?@>3@0<C20==O, 28:>@8AB0==N 4>40B:>28E ?5@5<V==8E 4;O 715@V30==O 40=8E 74V9A=NTBLAO >48= ?5@53;O4 ?5@28==>3> B5:ABC. <5==89 0:B0=B A1 =0 ?5@H><C 5B0?V 70?>2=NTBLAO >4=8< 5;5<5=B><  ?>=OBBO< N1, 0;5 =0 4@C3><C 5B0?V 4> =L>3> 4>40NBLAO <>6;82V 4>40B:>2V 5;5<5=B8, O:V A:;040NBL B5@<V=>;>3VG=5 ?>=OBBO. 0O2=VABL >=B>;>3VW ?@54<5B=>W 30;C7V =0 FVTW AB04VW <0T A?@8OB8 71V;LH5==N O:>ABV 9 H284:>ABV V45=B8DV:0FVW B5@<V=0. 0 4@C3><C 5B0?V 0=0;V7 >@83V=0;L=>3> B5:ABC 2V41C20TBLAO 70 1;>:0<8: A?>G0B:C ?>HC: 5;5<5=BV2 0:B0=B=>3> ;0=FN6:0 7;V20, ?>BV<  A?@020. ;O ?>1C4>28 ;0=FN6:0 ?@>2>48BLAO AB0B8AB8G=>-48AB@81CB82=89 0=0;V7 :>=B0:B=> @>7B0H>20=8E 5;5<5=BV2 (A;V2) ?5@28==>3> B5:ABC. @8B5@VT< 2V41>@C 5;5<5=BV2 2 0:B0=B=89 ;0=FN6>: A;C3CT B0: 720=89 :>5DVFVT=B ?>2B>@N20=L (k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s1)={V(m1G1),A1(N(m4ls2)),A2(N(m5ls1)),A3(N(m4ls1) Adj N(m4ls1))} @>0=0;878@>20=K @57C;LB0BK ;5G5=8O @0:0 <>G52>3> ?C7K@O ! (s2)={V(m1G1),A1(N(m4ls2)),A2(N(m5ls1)),A3(N(m4ls1) Adj N(m4ls1))} @>0=0;878@>20=0 ?5@5A04:0 ?5G5=8. ! (s1)={V(m1G2),A1(N(m5ls1)),A2(N(m4ls1))} 7;>65=0 >@B>?548G5A:0O B@0=A?;0=B0F8O ?5G5=8. ! (s1)={V(m1G2),A1(Adj N(m5ls1)),A2(N(m4ls1))} @>0=0;878@>20=K ?@8G8=K ?>@065=8O ?5G5=8. ! (s1)={V(m1G2),A1(N(m4ls2)),A2(N(m5ls1)),A3(N(m4ls1))} !D>@<C;8@>20=0 B5>@8O A5B59 5B@8. ! (s1)={V(m1G2),A1(N(m4ls2)),A2(N(m4ls1))(N(m4ls1))} @>45<>=AB@8@>20=> ?@8<5=5=85 A5B59 5B@8. ! (s2)={V(m1G2),A1(N(m5ls2)),A2(N(m4ls1))(N(m4ls1))} G5284=8< T B5, I> BCB <0T <VAF5 C7030;L=5==O-:><?@5AVO, 0 =5 2;0A=5 C7030;L=5==O, O:5 2V41C20TBLAO 2 ?@>F5AV V=B5;5:BC0;L=>3> @5D5@C20==O.   K = 20% 0;. 3.8 57C;LB0B8 5:A?5@8<5=B0;L=V9 ?5@52V@:8 ! 1 (>@83V=0;L=89 B5:AB 9 B5:AB @5D5@0BC)   K = 15%   ! K = 20%    k = 20%  k = 30% 0;.. 3.11 57C;LB0B8 5:A?5@8<5=B0;L=V9 ?5@52V@:8 ! 4 (>@83V=0;L=89 B5:AB 9 B5:AB @5D5@0BC) # @57C;LB0BV ?5@52V@:8 0;3>@8B<C 70 4>?><>3>N ?@>3@0<8 2B>@5D5@0B 1C;> 7@>1;5=89 =0ABC?=89 7030;L=89 28A=>2>:: ;3>@8B<, ?>1C4>20=89 =0 >A=>2V <>45;V C7030;L=5==O, 4>72>;OT =0 28E>4V >B@8<0B8 ?>2=>FV==C @5D5@0B82=C :>=AB@C:FVN, I> 2>;>4VT 2AV<0 =5>1EV4=8<8 4;O 28:>=0==O V=48:0B82=>W DC=:FVW 2;0AB82>ABO<8, BV;L:8 C @07V 28:>@8AB0==O >=B>;>3V9, AB2>@5=8E 4;O A8AB5<  . "0:8< G8=><, =0ABC?=8< :@>:>< C 4>A;V465=V C7030;L=5==O 2 ?@>F5AV @5D5@C20==O 4;O C4>A:>=0;5==O A8AB5<8   T <>45;N20==O 72 O7:V2  ?5@28==89 B5:AB  B5:AB @5D5@0BC  703>;>2>: 7 B>G:8 7>@C A0<5 C7030;L=5==O 9 AB2>@5==O =5>1EV4=8E >=B>;>3V9. 8A=>2:8 ;O ?>1C4>28 <>45;V C7030;L=5==O 2 A8AB5<V @5D5@C20==O D>@<0;L=> >?8A0=> >1'T:B 4>A;V465==O  @5D5@0B  B5:AB, I> A:;040TBLAO 7 =01>@C @5G5=L 287=0G5=>3> B8?C. ;O D>@<0;V70FVW 284V;5=>3> >1'T:B0 2 @>1>BV 28:>@8AB>2CTBLAO <5B>4, ?@8 O:><C >1'T:B 4>A;V465==O >?8ACTBLAO =5 2AVTN @V7=><0=VB=VABN V=D>@<0FVW, O:V 9>3> E0@0:B5@87CT, 0 =01>@>< V=20@V0=B=8E >7=0:, I> E0@0:B5@87CNBL @5D5@0B O: @57C;LB0B C7030;L=5==O 28EV4=>3> B5:ABC. ;O @5D5@0BC @5;520=B=8<8 T A8=B0:A8G=V, A5<0=B8G=V V, G0AB:>2>, 3@0<0B8G=V 72'O7:8 7 28EV4=8< B5:AB><. >@D>;>3VG=89 0=0;V7 C 40=><C 4>A;V465==V 72>48BLAO 4> 0=0;V7C 9 >?8AC 3@0<0B8G=8E 7=0G5=L 0:B0=BV2 V A8@:>=AB0=BV2 @>73;O=CB8E A8=B0:A8G=8E :>=AB@C:FV9, 0 B0:>6 4> G0AB:>2>3> <>@D5<=>3> (A;>2>B2>@G>3>) 0=0;V7C ?@548:0BV2 =0 ?@54<5B =0O2=>ABV 2 =8E D>@<0;L=8E >7=0: C7030;L=5==O. =0;V7 3@0<0B8G=8E V A;>2>B2>@G8E E0@0:B5@8AB8: 5;5<5=BV2 @5D5@0B82=8E :>=AB@C:FV9 C ?@>F5AV ?>1C4>28 A8=B0:A8G=>W <>45;V @5D5@0BC ?>:0702, I> 3@0<0B8G=V 7=0G5==O ?@548:0BV2, 0:B0=BV2 V A8@:>=AB0=BV2, I> 2E>4OBL 4> A:;04C @5G5=L B8?>2>W , >1<56CNBLAO GVB:> 287=0G5=8< =01>@><. >@D5<=89 0=0;V7 4VTA;V2 V :>@>B:8E ?@8:<5B=8:V2, I> 28ABC?0NBL C @>;V ?@8AC4:0 @5D5@0B82=8E A8=B0:A8G=8E :>=AB@C:FV9, 28O282, I> WE ?@5DV:A8 <0NBL 287=0G5=V 7=0G5==O, O:V ?V4A8;NNBL A5<0=B8:C @57C;LB0B82=>ABV, >4=0: WE =0O2=VABL =5 T >1>2'O7:>2>N D>@<0;L=>N >7=0:>N ?@8AC4:0 @5D5@0B82=>W :>=AB@C:FVW. >45;L C7030;L=5==O 2 ?@>F5AV @5D5@C20==O =0 A8=B0:A8G=><C @V2=V O2;OT A>1>N 42V B8?>2V @5D5@0B82=V A8=B0:A8G=V :>=AB@C:FVW, I> 2>;>4VNBL A5<0=B8:>N @57C;LB0B82=>ABV. "8?>289 V=48:0B82=89 @5D5@0B A:;040TBLAO 7 >4=>3>  B@L>E @5G5=L, O:V ?@54AB02;ONBL A>1>N 20@V0=B8 ?>H8@5==O 40=8E A8=B0:A8G=8E :>=AB@C:FV9. >45;L C7030;L=5==O A<8A;C 2 ?@>F5AV @5D5@C20==O =0 A5<0=B8G=><C @V2=V <VAB8BL C A>1V B@8 ?V4@V2=V: A5<0=B8:>-A8=B0:A8G=89, 2;0A=5 A5<0=B8G=89 V ;5:A8:>-A5<0=B8G=89: 0 A5<0=B8:>-A8=B0:A8G=><C @V2=V 2V41C20TBLAO ?>40==O A5<0=B8G=>W AB@C:BC@8 @5G5=L, O:V 2E>4OBL 4> A:;04C @5D5@0B82=>3> B5:ABC, C 283;O4V =01>@C 5;5<5=BV2: ?@548:0B0, >1'T:B0, I> T 3@0<0B8G=8< AC1'T:B><, 0:B0=BV2 V A8@:>=AB0=BV2. 0 2;0A=5 A5<0=B8G=><C @V2=V 2V41C20TBLAO ?>40==O @5D5@0BC C 283;O4V =01>@C @5G5=L V7 A5<0=B8G=8< 7=0G5==O< >1'T:B 01> @57C;LB0B 4>A;V465==O. 0 ;5:A8:>-A5<0=B8G=><C @V2=V 2V41C20TBLAO ?>40==O @5G5=L @5D5@0BC C 283;O4V 0:B0=B=8E AB@C:BC@, 70?>2=N20=8E ;5:A5<0<8 7 >@83V=0;L=>3> B5:ABC. #7030;L=5==O A<8A;C 2V41C20TBLAO 70 @0EC=>: 70?>2=5==O 0:B0=BV2 ;5:A5<0<8 7 287=0G5=8< <5B07=0G5==O<, O:V >?8ACNBLAO 70 4>?><>3>N >=B>;>3VW 25@E=L>3> @V2=O (A;>2=8: :0B53>@V9), 0 B0:>6 70?>2=5==O A8@:>=AB0=BV2 V ?>H8@5==O V<5==8E 0:B0=BV2 ;5:A5<0<8 7 >FV=>G=8< 7=0G5==O<. 0 >A=>2V 70?@>?>=>20=>W <>45;V C7030;L=5==O 1C2 ?>1C4>20=89 0;3>@8B< @5D5@C20==O 4;O 02B><0B8G=>W A8AB5<8. !B2>@5=0 4;O ?5@52V@:8 @>1>B8 FL>3> 0;3>@8B<C 5:A?5@8<5=B0;L=0 02B><0B8G=0 A8AB5<0 @5D5@C20==O  2B> 5D5@0B ?@>45<>=AB@C20;0 <>6;82VABL ?@0:B8G=>3> 28:>@8AB0==O <>45;V 9 0;3>@8B<C C 28?04:C =0O2=>ABV >=B>;>3V9 2V4?>2V4=8E 30;C759. , !  >A=>2C VA=CNG8E A8AB5< 02B><0B8G=>3> @5D5@C20==O ?>:;045=V AB0B8AB8G=V 9 ?>78FV9=V <5B>48 02B><0B8G=>3> @5D5@C20==O, I> 72>4OBLAO 4> 02B><0B8G=>3> 5:AB@03C20==O >:@5<8E @5G5=L, B5<0B8G=> V ;>3VG=> =5 ?>2'O70=8E <V6 A>1>N. !B2>@5==O 28A>:>O:VA=>3> 02B><0B8G=>3> @5D5@0BC ?@8?CA:0T ?@>2545==O AC?5@A8=B0:A8G=>3> 0=0;V7C ;>3V:>-A<8A;>2>W AB@C:BC@8 B5:ABV2, C7030;L=5==O A<8A;C V =0O2=>ABV 2 A8AB5<V 4;O WE 74V9A=5==O @>728=CB8E A;>2=8:>28E 70A>1V2 V >=B>;>3V9. >4=5 7 F8E 70240=L AL>3>4=V 2 ?>2=><C >1AO7V =5 28@VH5=5. #7030;L=5==O 2 ?@>F5AV @5D5@C20==O 2V41C20TBLAO =0 45:V;L:>E @V2=OE: A8=B0:A8G=><C, A5<0=B8G=><C V, G0AB:>2>, 3@0<0B8G=><C. 0 :>6=><C @V2=V 2V41C20TBLAO >1'T4=0==O B8?>28E 4;O @5D5@0B82=8E :>=AB@C:FV9 >1'T:BV2 (A8=B0:A8G=8E :>=AB@C:FV9, ;5:A5<, <>@DV2) C :;0A8 =0 >A=>2V 7030;L=8E 4;O =8E 2;0AB82>AB59. >45;L C7030;L=5==O A<8A;C 2:;NG0T 2 A515 <>45;L ?@54AB02;5==O 7=0=L, ?>1C4>20=C =0 107V >=B>;>3V9. # 40=><C 4>A;V465==V <>45;N20==O ?@>F5AC C7030;L=5==O 72>48BLAO 4> ?>1C4>28 <>45;V @5D5@0BC O: =01>@C B8?>28E 4;O V=48:0B82=8E @5D5@0BV2 A8=B0:B8:>-A5<0=B8G=8E :>=AB@C:FV9 (AB@C:BC@) V7 7030;L=8< <5B07=0G5==O< V 4> =0ABC?=>3> 7<VAB>2>3> :>=AB@CN20==N @5D5@0BC: =0?>2=5==O A8=B0:A5<, O:V 2E>4OBL C <>45;L, ?>=OBBO<8 2V4?>2V4=8E :;0AV2. =0;V7 3@0<0B8G=8E V A;>2>B2>@G8E E0@0:B5@8AB8: 5;5<5=BV2 @5D5@0B82=8E :>=AB@C:FV9 C ?@>F5AV ?>1C4>28 A8=B0:A8G=>W <>45;V @5D5@0BC ?>:0702, I> 3@0<0B8G=V 7=0G5==O ?@548:0BV2, 0:B0=BV2 V A8@:>=AB0=BV2, I> 2E>4OBL 4> A:;04C @5G5=L B8?>2>W @5D5@0B82=>W :>=AB@C:FVW, >1<56CNBLAO GVB:> 287=0G5=8< =01>@><. >@D5<=89 0=0;V7 4VTA;V2 V :>@>B:8E ?@8:<5B=8:V2, I> 28ABC?0NBL C @>;V ?@8AC4:0 @>AV9AL:><>2=8E @5D5@0B82=8E A8=B0:A8G=8E :>=AB@C:FV9, 28O282, I> WE ?@5DV:A8 <0NBL 287=0G5=V 7=0G5==O, O:V ?V4A8;NNBL A5<0=B8:C @57C;LB0B82=>ABV, >4=0: WE =0O2=VABL =5 T >1>2'O7:>2>N D>@<0;L=>N >7=0:>N ?@8AC4:0 @5D5@0B82=>W :>=AB@C:FVW. >45;L C7030;L=5==O 2 ?@>F5AV @5D5@C20==O =0 A8=B0:A8G=><C @V2=V O2;OT A>1>N 42V B8?>2V @5D5@0B82=V A8=B0:A8G=V :>=AB@C:FVW, I> <0NBL A5<0=B8:C @57C;LB0B82=>ABV. "8?>289 V=48:0B82=89 @5D5@0B A:;040TBLAO 7 >4=>3>  B@L>E @5G5=L, O:V T 20@V0=B0<8 ?>H8@5==O 40=8E A8=B0:A8G=8E :>=AB@C:FV9. >45;L C7030;L=5==O A<8A;C 2 ?@>F5AV @5D5@C20==O =0 A5<0=B8G=><C @V2=V <VAB8BL C A>1V B@8 ?V4@V2=O: A5<0=B8:>-A8=B0:A8G=89, 2;0A=5 A5<0=B8G=89 V ;5:A8:>-A5<0=B8G=89. 0 A5<0=B8:>-A8=B0:A8G=><C @V2=V 2V41C20TBLAO ?>40==O A5<0=B8G=>W AB@C:BC@8 @5G5=L, O:V 2E>4OBL 4> A:;04C @5D5@0B82=>3> B5:ABC, C 283;O4V =01>@C 5;5<5=BV2: ?@548:0B0, >1'T:B0, I> T 3@0<0B8G=8< AC1'T:B><, 0:B0=BV2 V A8@:>=AB0=BV2. 0 2;0A=5 A5<0=B8G=><C @V2=V 2V41C20TBLAO ?@54AB02;5==O @5D5@0BC C 283;O4V =01>@C @5G5=L V7 A5<0=B8G=8< 7=0G5==O< >1'T:B 01> @57C;LB0B 4>A;V465==O. 0 ;5:A8:>-A5<0=B8G=><C @V2=V 2V41C20TBLAO ?>40==O @5G5=L @5D5@0BC C 283;O4V 0:B0=B=8E AB@C:BC@, 70?>2=N20=8E ;5:A5<0<8 7 >@83V=0;L=>3> B5:ABC. #7030;L=5==O 7<VABC 2V41C20TBLAO 70 @0EC=>: 70?>2=5==O 0:B0=BV2 ;5:A5<0<8 7 287=0G5=8< <5B07=0G5==O<, O:V >?8ACNBLAO 70 4>?><>3>N >=B>;>3VW 25@E=L>3> @V2=O (A;>2=8: :0B53>@V9), 0 B0:>6 70?>2=5==O A8@:>=AB0=BV2 V ?>H8@5==O V<5==8E 0:B0=BV2 ;5:A5<0<8 7V 7=0G5==O< >FV=>G=>3> C7030;L=5==O. 10. 0 >A=>2V 70?@>?>=>20=>W <>45;V C7030;L=5==O 1C2 ?>1C4>20=89 0;3>@8B< @5D5@C20==O 4;O 02B><0B8G=>W A8AB5<8. !B2>@5=0 4;O ?5@52V@:8 @>1>B8 FL>3> 0;3>@8B<C 5:A?5@8<5=B0;L=0 02B><0B8G=0 A8AB5<0 @5D5@C20==O  2B> 5D5@0B ?@>45<>=AB@C20;0 <>6;82VABL ?@0:B8G=>3> 28:>@8AB0==O <>45;V 9 0;3>@8B<C. !!  !"%   PAGE  PAGE 8 PAGE  PAGE 41 PAGE  PAGE 125 . ;N<5=0C . . $C=:F88 >17>@>2 2 A8AB5<5 =0CG=KE :><<C=8:0F89.  "@C4K  8<. .. @C?A:>9, 1976, ". 29.  !. 233  244. . ;N<5=0C . . @>1;5<K A25@BK20=8O =0CG=>9 8=D>@<0F88.  .: 0C:0, 1982.  166 A. . ;N<5=0C . ., 5>=>2 . ., '038=0 . . @>1;5<K 0==>B8@>20=8O 8 @5D5@8@>20=8O =0CG=>9 ;8B5@0BC@K // =0;87 2708<>A2O759 181;8>B5G=>-181;8>3@0D8G5A:8E 48AF8?;8= A 8=D>@<0B8:>9 /  8<. . . @C?A:>9.  ., 1982.  125 A. . !>;>2L52 . . !>AB02;5=85 8 @540:B8@>20=85 @5D5@0B>2: >?@>AK B5>@88 8 ?@0:B8:8. 0=@K 8=D>@<0F8>==>9 ;8B5@0BC@K: 17>@. 5D5@0B.  .: =830, 1983.  320 A. . >;:>20 . .  2>?@>AC > @5D5@8@>20=88 =0CG=>-B5E=8G5A:>9 ?5@8>48:8 2 @5D5@0B82=>< 6C@=0;5 " // ". !5@. 1.  1970.  ! 5.  !. 24  25. . >@L:>20 . . >A>185 ?> @5D5@8@>20=8N 8 @540:B8@>20=8N =0CG=>-B5E=8G5A:>9 ;8B5@0BC@K (!?@02>G=8: 4;O @540:B>@>2, @5D5@5=B>2 8 :>@@5:B>@>2).  ., 1964.  268A. . 5>=>2 .. 5D5@8@>20=85 8 0==>B8@>20=85 =0CG=>-B5E=8G5A:>9 ;8B5@0BC@K / B2. 54. .!. ;5?>2;  !!! , !81. >B4-=85, >A. ?C1;. =0CG.-B5E=. 1-:0.  >2>A818@A:: 0C:0. !81. >B4-=85, 1986.  172 A. . (025@4>20 ..  2>?@>AC >1 >?B8<0;L=>9 AB@C:BC@5 @5D5@0B0 // 5D5@8@>20=85 2 >1I5AB25==KE =0C:0E.  ., 1982.  !. 101  114. . C;8: . . 5D5@0B =0CG=>3> 4>:C<5=B0 2 548=>9 8=D>@<0F8>==>9 A5B8 // ". !5@. 1.  1971.  ! 1.  !. 28  32. . >@L:>20 . ., >@>E>2 -. . 5D5@0B 2 A8AB5<5 =0CG=>9 :><<C=8:0F88. 0?@02;5=8O A>25@H5=AB2>20=8O ;8=328AB8G5A:8E 8 AB@C:BC@=KE E0@0:B5@8AB8: // B>38 =0C:8 8 B5E=8:8. !5@. =D>@<0B8:0. ". 11.  .: ", 1987.  232 A. . %09@>20 .$., (0@>=>20 .. 2B><0B878@>20==K5 8=D>@<0F8>==K5 181;8>B5G=K5 A8AB5<K: 7040G8 >1@01>B:8 8=D>@<0F88: >=>3@0D8O.  %., 2002.  120 A. . 40=>20 . !.  =0CG=KE >A=>20E <5B>48:8 @5D5@8@>20=8O. // ". !5@ I.  1967.  ! 2.  !. 12  16. . 5>=>2 ..  <5B>40E 02B><0B8G5A:>3> @5D5@8@>20=8O (!(, 1958  1974 33.) // ". !5@. II.  1975.  ! 6.  !. 16  20. . AK:0 .$. 17>@ 8AA;54>20=89 ?> 02B><0B8G5A:>9 >1@01>B:5 5AB5AB25==>3> O7K:0 2 !( // @>1;5<K 18>=8:8: 5A?. <564C254. =0CG.-B5E. A1.  %.: 8I0 H:. 74-2> ?@8 %0@L:. #=-B5, 1985.  K?. 34, !. 3  18. . 8@> .. 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"5>@5B8G5A:85 ?@>1;5<K ?0;5>1>B0=8:8.  .: 0C:0, 1990.  285 A. . >@>1:>2 .. 0;5>=B>;>38G5A:85 >?8A0=8O: (5B>4. ?>A>185).  .: 54@0, 1971.  200 A. . 8==59 . $8;>A>D8O 1>B0=8:8.  .: 0C:0, 1989.  452 A. . @O7=CE8=0 ".. 1I85 ?@8=F8?K ?>AB@>5=8O 02B><0B8G5A:>3> A8=B0:A8G5A:>3> 0=0;870B>@0 / !8=B0:A8G5A:89 0=0;87 =0CG=>3> B5:AB0 =0 -.  .: 0C:>20 C<:0, 1999.  !. 6  39. . >@D>;>38G5A:89 0=0;87 =0CG=>3> B5:AB0 =0 - / .. 5@5159=>A, ".. @O7=CE8=0, .. 0@GC: 8 4@.; B2. @54. ".. @O7=CE8=0;  #!! . =-B O7K:>2545=8O 8<. .. >B51=8.  852: 0C:. 4C<:0, 1989.  264 A. . 2B><0B870F8O 0=0;870 =0CG=>3> B5:AB0.  .: 0C:. 4C<:0, 1984.  257A. . 0I5=:> .., =>@8=0 .., >;G0=>20 ".., '5?83> ".!., (C<8;8=0 .., /@>25=:> .. @>1;5<K 02B><0B870F88 8=45:A8@>20=8O 8 @5D5@8@>20=8O // B>38 =0C:8 8 B5E=8:8. !5@. =D>@<0B8:0; ".7  .: " !!! , 1983.  !. 7  164. . CAA:0O 3@0<<0B8:0.  .: 0C:0, 1980.  ". I.  784 A. . /:>25=:> .., 070@5=:> .. 1>1I5=85 =0 <>@D>;>38G5A:>< C@>2=5 2 ?@>F5AA5 @5D5@8@>20=8O // 5AB=8: !#.  2001.  !6.  !. 45  46. . ;8<5=:> .$. /: =0@>46CTBLAO A;>2>: 0C:.-?>?C;. 284.  .: O4. H:., 1991.  288 A. . 070@5=:> .. 0B5<0B8G5A:85 <>45;8 ?@5D8:A0;L=>3> A;>2>>1@07>20=8O 8 8E 8A?>;L7>20=85 2 A8AB5<0E 02B><0B8G5A:>9 >1@01>B:8 B5:AB>2 =0 @CAA:>< O7K:5: 8A& :0=4. B5E=. =0C:: 05.13.01.  %., 1984.  203A. . 2B><0B870F8O 0=0;870 =0CG=>3> B5:AB0.  .: 0C:. 4C<:0, 1984.  257A. . CAA:0O 3@0<<0B8:0.  .: 0C:0, 1980.  ". II.  710 A. . /:>25=:> .. >45;L A8=B0:A8G5A:>3> >1>1I5=8O 2 ?@>F5AA5 @5D5@8@>20=8O // 5AB=8: !#.  2002.  !3.  !. 17  19. . 0:>=><5@=>AB8 AB@C:BC@=>9 >@30=870F88 =0CG=>-@5D5@0B82=>3> B5:AB0.  .: 0C:>20 4C<:0, 1982.  322 A. . 8=328AB8G5A:85 ?@>1;5<K 02B><0B870F88 @540:F8>==>-8740B5;LA:8E ?@>F5AA>2.  .: 0C:>20 4C<:0, 1986.  230 A. . 528F:89 ... A=>2K B5>@88 A8=B0:A8A0.  >A:20: # !!, 2002.  234A. . /:>25=:> .. !5<0=B8G5A:>5 8 A8=B0:A8G5A:>5 >1>1I5=85 2 ?@>F5AA5 @5D5@8@>20=8O // G5=V 70?8A:8 %0@:V2AL:>3> 3C<0=VB0@=>3> V=AB8BCBC  0@>4=0 C:@0W=AL:0 0:045<VO .  %.: :>, 2001.  !. 446  450.  5@5189=VA .. !B0B8AB8G=V <5B>48 4;O ;V=32VABV2: 02G0;L=89 ?>AV1=8: / V==8FO:  >20 =830 , 2001.  168 A. . $0D5=15@35@ ., #>;; . ">;:>2K9 A;>20@L ?> :><?LNB5@=K< B5E=>;>38O< 8 Internet. 6-5 8740=85.  .: 80;5:B8:0, 1996.  480 A. . 8=328AB8G5A:89 M=F8:;>?548G5A:89 A;>20@L / ;. @54. . . /@F520.  .: !>2. -=F8:;>?548O, 1990.  685 A. . 09715@3 . ., >7>2A:89 . (., !B0@>4C1F520 . . !>2@5<5==K9 M:>=><8G5A:89 A;>20@L.  .: $ -, 1996.  496 A. . !>F8>;>38G5A:89 M=F8:;>?548G5A:89 A;>20@L =0 @CAA:><, 0=3;89A:><, =5<5F:><, D@0=FC7A:>< 8 G5HA:>< O7K:0E. 540:B>@-:>>@48=0B>@  0:045<8:  . . A8?>2.  .: 740B5;LA:0O 3@C??0 $ -  , 1998.  488 A. . @0B:0O <548F8=A:0O M=F8:;>?548O.  2-E B><0E / >4 @54. :045<8:0  . . >:@>2A:>3>.  .:  548F8=A:0O M=F8:;>?548O, @>=-@5AA, 1994. . 070@5=:> .., >?>20 ".. =0;V7 A<8A;>2>W AB@C:BC@8 703>;>2:0 O: B5:ABC 7 <0:A8<0;L=8< @V2=5< C7030;L=5==O // @>1;5<8 A5<0=B8:8 A;>20, @5G5==O B0 B5:ABC: 1V@=8: =0C:>28E ?@0FL. 8?CA: 12 / V4. @54. .. >@1>75@>20.  .: #, 2004.  !. 143  149. !! C !!  @  @5G5==O A  A;>2> 0;. 1.5. V4 A<8A;C @5G5==O 4> A<8A;C A;>20 70 6. ABV=>< '/ C '/  0;. 1.4. A524>@5G5==O 70 . 0@=0?><  !"!!# '/ ! !/""/ ! '/ ! /""/ ! /""/ !/""/ 0;.. 1.3. A524>?>=OBBO 70 . 0@=0?>< '/ /""/ ! 0;.. 1.2 87=0G5==O ?>=OBBO A<8A;C 70 . $@535 I!"I!", I!"I!", "" x $ &I/ $ &I/ x # !! !! x '/  x !"  "!" !! 1 !! 2 $ " =0;V7 #7030;L=5==O !8=B57 $ " "!"    8A. 2.2. #7030;L=5==O   8A. 2.3. 1<565==O 0;. 2.4 =B>;>3VO 25@E=L>3> @V2=O 5 2 9 3 !2(s1)={Sr(g16),V(m1g13g22g32g41),A1(VmiVlsjg11g71),Ai(VmiVlsjg11g71} i=4 j=1 i=4 j=1 3 6 2 9 3 !2(s2)={Sr(g16),V(Vmi g13g22g32g41),A1(VmiVlsjg11g71),Ai(VmiVlsjg11g71} i=2 i=4 j=1 i=4 j=1 3 6 2 9 3 !1(s2)={Sr(g16),V(Vmi g14g21g32g42g82),A1(VmiVlsjg11g71),Ai(VmiVlsjg11g71} i=2 i=4 j=1 i=4 j=1 5 2 9 3 !1(s1)={Sr(g16),V(m1g14g21g32g42g82),A1(VmiVlsjg11g71),Ai(VmiVlsjg11g71} i=4 j=1 i=4 j=1 2 R={!(s1), !(V si), !(s2)}, i=1 2 7 O2(R,S) = {Sr,VVi,A1,VAn} = i=1 i=2 3 2 6 2 9 3 = {Sr(g16), V(VmiVGj), A1(VmiVlsjg11g71), An(VmiVlsjg11g71} i=1 j=1 i=4 j=1 i=4 j=1 7 CK(SSS)={Sr, Vi, A1, VAi} i=2 9 3 Ls = (V mi V lsj) i=1 j=1 0;. 3.4 5:A8:>-A5<0=B8G=0 :;0A8DV:0FVO V<5==8E 3@C?, I> 70?>2=NNBL V<5==V 0:B0=B8  N(m9 ls2 g11g74) N(m8 ls2 g11g73) N(m7 ls2 g11g72) N(m6 ls2 g11g72) N(m6 ls2 g11g71) N(m5 ls2 g11g72) N(m5 ls2 g11g71) N(m5 ls1 g11g72) N(m5 ls1 g11g71) N(m4 ls2 g11g72) N(m4 ls2 g11g71) N(m4 ls1 g11g72) N(m4 ls1 g11g71) N(m9 ls3) N(m7 ls2) N(m8 ls2) N(m6 ls2) N(m5 ls2) N(m5 ls1) N(m4 ls2) N(m4 ls1) N(m9) N(m8) N(m7) N(m6) N(m5) N(m4) N 4 G =(g11 V g7i) i=1 CK=(Sr,Vi, A1, A2 & , A7), 2 R={!(s1), !(V si), !(s2)} i=i 7 !(SSS)={Sr, Prd, Obj, VAi}, i=2 28EV4 "  B5:AB   703>;>2>: f  01A>;NB=0 G0AB>B0 m  :V;L:VABL A;V2 C 703>;>2:C i, j  4>?><V6=V V=45:A8 0;. 3.6 B0? 1 0;3>@8B<C @5D5@C20==O B0: N1= (index) G0AB>B0=max B0: max=f index=j =V =V j<m f>max =V B0: :V=5FL B5:ABC =V B0: f=f+1 T(i)=(j) i=i+1 i=0 f=0 j=j+1 0;. 3.5 A=>2=V 5B0?8 0;3>@8B<C 02B><0B8G=>3> @5D5@C20==O B0? 3 B0? 2 B0? 1 AB0B>G=0 ?>1C4>20 @5D5@0B82=>W :>=AB@C:FVW >1C4>20 0:B0=B=>3> ;0=FN6:0 >HC: N1 5 ss =(V ssi) i=1 2 2 6 6 ss5=VV v NN v AdjAdj v SrSr=V(VGi)V(VGi)vN(VGi)N(VGi)vAdj(G7)Adj(G7)v i=1 i=1 i=3 i=3 Sr(G8)Sr(G8)=V((g14g21g32g42g82) v (g13g22g32g41))V((g14g21g32g42g82) v 4 4 (g13g22g32g41)) v N(g11(V g7i))N(g11(V g7i))v Adj(g12g81)Adj(g12g81) v Sr(g16)Sr(g16) i=1 i=1 2 2 2 ss4=SrV v VN=Sr(G8)V(VGi) v V(V Gi)N(G5) v V(V Gi)N(G4) = i=1 i=1 i=1 = Sr(g16)V((g14g21g32g42g82)v(g13g22g32g41)) v V((g14g21g32g42g82)v(g13g22g32g41))N(g11g73) v V((g14g21g32g42g82)v(g13g22g32g41))N(g11g74) 2 ss3=VSbj=V(V Gi)N(G3)=V(( g14g21g32g42g82)v(g13g22g32g41))N(g11g71), i=1 4 2 ss2=NN=N(V Gi)N(G4 v G6)= N(g11(V g7i))N((g11g72)v(g11g74)), i=3 i=1 6 4 ss1=AdjN=Adj(G7)N(V Gi)= Adj(g12g81)N(g11(V g7i)), i=3 i=1 6 3 A2=AdjN, A3=NN, 345 N=(V Gi)=g11(V g7i), Adj=G7=(g12g81) i=3 i=1 5 3 A1=N, 345 N=(V Gi )= g11(V g7i) i=3 i=1 (3.4) !2=Sr(g16)V2(g13g22g32g41)A1((g12g81)(g11g71))A2((g12g81)(g11g72)) A3((g12g81)(g11g72))A4((g12g81)(g11g73(2)))A5((g12g81)(g11g72)) A6((g12g81)(g11g72))A7((g12g81)(g11g72(4))) (3.3) !2 =Sr(G8)V2(G2)A1((G7)(G3))A2((G7)(G4))A3((G7)(G4)) A4 ((G7)(G5(4)))A5 ((G7)(G4))A6 ((G7)(G4))A7((G7)(G4(6))) (3.2) !1=Sr(g16)V1(g14g21g32g42g82)A1((g12g81)(g11g71))A2((g12g81)(g11g72))A3((g12g81)(g11g72))A4((g12g81)(g11g73(2)))A5((g12g81)(g11g72)) A6 (g12g81)(g11g72))A7((g12g81)(g11g72(4))) (3.1) !1=Sr(G8) V1 (G1) A1 ((G7)(G3)) A2 ((G7)(G4)) A3 ((G7)(G4)) A4 ((G7)(G5(4))) A5 ((G7)(G4)) A6((G7)(G4)) A7 ((G7)(G4(6))) 0;. 3.1 #7030;L=5==O =0 A8=B0:A8G=><C @V2=V R " !K1 !K2 !K1 !K2 !K3 !K4 !K5 #,/ 8 G=V Gi i=1 1, O:I> ! 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