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"#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # D.5E(3325&%+# Je( )%#(!(0*(#&B#A%23( ! )%(&#(1"3-0$$'F*(#(0*(G%7#97.-&%.9(R(!#"#$#S(-3*-%((!#"# $(#(!v( !(#(!vQ(%,(&#(1#"2%('5d0'%"-#(-%(&#(1"3-0$$'F*(%(( $(#(!vQ(&#(1#"2%(-%"%$+#(-%(&#(1"3-0$$'F*( ! )%("%1"%,%*2#($363T((((!#334#$# !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # @%.2F)32G&#E2.%31)# Jf( ! )%#(!(0*(#&B#A%23( ! )%#(R(!"#$#S(0*#((1"3-0$$'F*(,3A"%(1#&#A"#,(-%(!Q(jTT[G( ! )%#*(O(G(x(-3,(1#&#A"#,(,3A"%(!(R':%((OQ(x(#(!vS( ( )%(-'$%( 56#70#879,:2;,<=#8,97;>2#87#:?(((F( (5:#@9A8B;7#8,97;>217=>7#6?##O(.(x((( #56#07#978B;7#8,97;>217=>7#2#:?# ,'(/(-3,(1#&#A"#,(5(Q(0(#(!v(2#&%,(d0%((O([(5ljl0((G(((x([(5lGl0( KZOZ,!O2Z# )'(j(TT[(G((%,(0*#(1"3-0$$'F*(,3A"%(!(("(j(.(G(( R0*#("%/&#(-%(%,$"'20"#(%,(0*#(-%"'O#$'F*(-'"%$2#S( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # @%.2F)32G&#E2.%31)# Jg( ! )%#(!(%&(#&B#A%23($#,2%&&#*3(-%(&#,(&%2"#,(6#Gb,$0&#,(( G(.7TT[=!(0*#(1"3-0$$'F*(,3A"%(!( W!=!44M(%,(-%"'O#$'F*(-'"%$2#(-%(W!.744M( RW!.744M(1"3-0$%(-'"%$2#6%*2%(W!=!44MS( ! t($3*(&#(1"3-0$$'F*(W!TT[h7(,3A"%(!( h7N!(%,(-%"'O#$'F*(-'"%$2#(-%(W!N!( 7H%61&3,( En el castellano no son así las cosas, existen las raíces. !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # @%.2F)32G&#E2.%31)# Jk( 7*(0*($3*H0*23(-%(1"3-0$$'3*%,( ! )%#( !( 0*( #&B#A%23( G( h( 0*( $3*H0*23( -%( 1"3-0$$'3*%,(,3A"%(!( ! )%#*(O(G(x(-3,(1#&#A"#,(,3A"%(!Q(OQ(x(#!v(( )%(-'$%(d0%(( Xx(%,(-%"'O#$'F*(-'"%$2#(-%(OY(( XO(1"3-0$%(-'"%$2#6%*2%(xY( Xx(,%("%-0$%(-'"%$2#6%*2%(#(OY( O(.(x( ,'(/(-3,(1#&#A"#,(5Q(0(#!v(2#&%,(d0%(O([(5ljl0((G(((x([(5lGl0(G(,%($061&%(=QCCSY>###A( !"# $% &' () *+ #! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # @%.2F)32G&# P_( ! )%#(!(0*(#&B#A%23(G(h(0*($3*H0*23(-%(1"3-0$$'3*%,(,3A"%(!( ! )%#*(:(G(6(-3,(1#&#A"#,(,3A"%(!Q(:Q(6(#!v(( )%(-'$%(d0%(( Xx(%,(-%"'O#$'F*(-%(OY(( XO(1"3-0$%(xY( Xx(,%("%-0$%(#(OY( O(m(.(x( ((0(_.#0Z( ((0Z(.#0J( (::::::::( (0*oZ(.#0*( (x(([(0*( ,'(/(0*#(,%$0%*$'#(L*'2#(-%(1#&#A"#,Q(0_Q(0ZQ(0JQ(:::0*(R*n_S(#!v(( 2#&%,(d0%(O([(0_( Derivación de longitud n ! "#$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # >%6)32G&#E%#HI(%# PZ( ! )%#(!(0*(#&B#A%23(G(h(0*($3*H0*23(-%(1"3-0$$'3*%,(,3A"%(!( ! )%#*(O(G(x(-3,(1#&#A"#,(,3A"%(!Q(%,(-%$'"(OQ(x(#!v(( )%(-'$%(d0%(%j',2%(0*#("%&#$'F*(-%(E+0%(%*2"%(O(G(x(G(,%("%1"%,%*2#( 13"(@#_.#c#,'(,%(O%"'L$#(d0%T( @#W.#c####E# @#S#c# A79G)-.%.-*# ! N%i%j'O#( ! E"#*,'DO#(( ! )'692"'$#(R%*(/%*%"#&(VM(,%($061&%S( 9#/#F&%#.-7)@%')E&#.-#49&3)<F.#$#9# *9&#)3F%4-*# !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # ->:?JHKL:<#4=>?:$7<# PJ( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # K%L*'$'3*%,( 8%"#"d0?#(-%(W+36,yG( z"A3&%,(-%(-%"'O#$'F*( PP( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # MN(O#%+#(&)#'.)/0123)P# P`( a*#(/"#6CD$#(-%,$"'A%(&#(%,2"0$20"#(-%( &#,( B"#,%,( G( -%( &#,( 1#&#A"#,( -%( 0*( &%*/0#H%(G(,%(#1&'$#(13"('/0#&(#T( ! 4#,(&%*/0#,(*#20"#&%,(+06#*#,( ! 4%*/0#H%,(-%(1"3/"#6#$'F*:( a*#(/"#6CD$#(%,(0*(X%*2%(B3"6#&Y(1#"#( %,1%$'L$#"(-%(6#*%"#(L*'2#(%&($3*H0*23( -%($#-%*#,(-%(,?6A3&3,(d0%($3*,D20G%*( 0*(&%*/0#H%:( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # -.)/0123)#E%6#L)+1%66)&5# Pc( Una gramática del castellano como diagrama sintáctico M"#$'F*( I*36'*#&( IO%"A#&( W361&%6%*23( #"<$0&3( O%"A3( ,0,2#*DO3( W361&%{$'"$( #"<$0&3( ,0,2#*DO3( I*36'*#&( 4#( ,#*/"%( $3""%( 13"( %&( "?3( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # >%'6)+#E%#B.5E(332G&# Pe( |M"#$'F*nTT[(|I*36'*#&n(|IO%"A#&n(}(|I*36'*#&n(|IO%"A#&n|W361&%6%*23n( |I*36'*#&nTT[(|)0,2#*DO3n(}(|V36h"n(}(|!"<$0&3n(|)0,2#*DO3n(( ( ((}(|!"<$0&3n(|)0,2#*DO3n(|!-H%DO3n( ( ((}(|!"<$0&3n(|)0,2#*DO3n(|!-H%DO3n( ( ((}(|(I*36'*#&(n-%(|(I*36'*#&(n( |IO%"A#&nTT[(|~%"An(}(|~%"An(|!-O%"A'3n(( |W361&%6%*23nTT[|W36K'"n(}|W36;*n(}|W36W'"n(}(|W36K'"n(|W36;*n(|W36W'"n(( |W36K'"nTT[(|I*36'*#&n(Q(|W36;*nTT[(#(|I*36'*#&n(}(1#"#(|I*36'*#&n(}(::::( |W36W'"n(TT[(%*(|I*36'*#&n(}(-%,-%(|I*36'*#&n(}($0#*-3(|I*36'*#&n(}(::::( K3*-%T (|)0,2#*DO3nQ(|!-H%DO3nQ(|!-O%"A'3nQ(|!"<$0&3nQ(|V36h"nQ(|~%"A3nQ(%2$(236#*( $363(O#&3"%,(1#&#A"#,(1"31'#,(-%(%,2#,($#2%/3"?#,(/"#6#D$#&%,(( a*#(/"#6CD$#(-%&($#,2%&&#*3(%*(*32#$'F*(-%(=#$y0,( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # @%A2&232G&# Pf( Como se determina (define) una gramática. Es una cuádrupla: (!T, !N, S, P), !T y !N son alfabetos: !T: Alfabeto de símbolos terminales. Todas las cadenas del lenguaje representado por la G (L(G)) están formadas con símbolos de este alfabeto. !N: Alfabeto de símbolos No Terminales. Conjunto de símbolos auxiliares introducidos como elementos auxiliares para la definición de G pero que no figuran en las cadenas de L(G). S: Axioma o símbolo destacado. Es un símbolo NT a partir del que se comienzan a aplicar las reglas de P. P: conjunto de reglas de producción: u::=v donde u#!+ y v#!* u = xAy tal que x, y #!* y A #!N.. !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # G = ({0,1}, {N,C}, N, P) P = {N::= NC, N::=C, C::= 0, C ::=1} @%A2&232G&# Pg( !T: Alfabeto de símbolos terminales( !T: Alfabeto de símbolos NO terminales( Axioma( Producciones( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # @%A2&232G&# Pk( )%($061&%(%*2"%(&3,(#&B#A%23,(-%(>T( !d#+#!D#[(!##!&B#A%23(3(O3$#A0&#"'3(-%(>(# !d#0#!D#S#*#(R,3*(-',H0*23,S( D9<%')E&#.-#5%'eF*T()'(0TT[O#G(0TT[(x(,3*(-3,("%/&#,(-%(1"3-0$$'F*( -%(hQ(%*23*$%,(,%(10%-%(%,$"'A'"(0(TT[(O(}(x( (( )%( -%*36'*#( *32#$'F*( 5DfT( CA912# DA912E# 87# F2;GB0# A# CA912# DA912E#87#F2;GB0.D2B9## ( 7H%61&3T( ,%#(>([(R\_QZQJQPQ`QcQeQfQgQk^Q(\VQK^Q(VQhS( (((((((h([(\(VTT[(VK((K(u(KTT[(_(Z(J(P(`(c(e(f(g(k^( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # 45./)#+%&1%&32)6#`_( )%#(0*#(HQ(,%#(!##(!vQ(%,(-%$'"(,%#(j(#(R(!E(a(!V(SvQ(j( ,%(-%*36'*#(;970%#*-&<-&')%4#.-#6(,'(,%(O%"'L$#T( $#_.#Q( %,(-%$'"Q(d0%(%j',2%(0*#(%&'()*+$!,&!-./&!%*2"%(%&(#j'36#(G(!:( )'( Q# #!d_# ,%( -'$%( d0%# Q# %,( 0*## $-&<-&')%# 9# )&*<7F'')E&# .-4# 4-&3F%R-#.-*'7)<9#G97#6( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # $%&'()*%#)+532)E5#)#(&)#'.)/0123)# `Z( )%#(&#(/"#6CD$#T( (>Z([(R!EQ(!VQ()Q(hS( ( )%(&#T( ( ( ( (&%*/0#H%(#,3$'#-3(#(>Z(( ( ( ( (&%*/0#H%(/%*%"#-3(13"(>Z(( ( ( ( (3(&%*/0#H%(-%,$"'23(13"(>Z( ( ( (( #&( $3*H0*23( (-%( 23-#,( &#,( ,%*2%*$'#,( R1#&#A"#,S(/%*%"#-#,( 13"(>ZQ(%,(-%$'"T( ( ( ( (4R>ZS([(\j(}()(#(vjQ(j(#(!vE^( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # >%3(.+2F2E)E# `J( )%#(H"# ! a*#(H(,%(&#(7-'F7*)@%#-�Q(I#!"DJQ(,'(,%($061&%T(( 0!1#!2!0!3## #( • )'(!#4#$#'I#K###I#$((,%(-'$%(d0%(H(%,(7-'F7*)@%#%#)/gF)-7.%*(( • )'($#4#$#'I#K##!#I((,%(-'$%(d0%(>(%,(7-'F7*)@%#%#.-7-'(%*( ! #a*#("%/&#(-%(1"3-0$$'F*(%,("%$0",'O#(,'(D%*%(&#(B3"6#T(( 0!445!2!0!3!! ! )'( 0*( &%*/0#H%( %,( '*L*'23Q( &#( /"#6CD$#( d0%( &3( "%1"%,%*2#( D%*%( d0%(,%"("%$0",'O#( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # K%L*'$'3*%,( 8%"#"d0?#(-%(W+36,yG( z"A3&%,(-%(-%"'O#$'F*( `P( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # ;%.).Q(R)#E%#LI5/+S,# ``( >(E;hM(P( >(E;hM(J( >(E;hM(Z( >(E;hM(_( >P()(>J(()(>Z()(>_( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # H2B5#T# `c( >[(R!EQ(!VQ()Q(hS( !E+!V([!Q(#&B#A%23(/"#6CD$#Q( !E0!V[(*( >_( V3(N%,2"'*/'-#,( 3($3*(7,2"0$20"#(-%(I"#,%( K9&#-*<7F'<F7%#.-#;7%*-*C( Rj!GTT[jOGS(#(hQ(-3*-%T( (((((((((jQG(#(!v(Q(!(#(!V(Q(O#!v( 7*(j!G(TT[(jOG(((($0#*-3(O[%Q(( j!G(TT[(jG("%/&#,($361"%,3"#,( 0#!m( O#!v(F#CCS#@( �*'$#("%,2"'$$'F*T(%CCS#@#-A# I3"6#(,%*2%*$'#&T( 0([(j!GQ(jQG#!vQ(!#!V( 7H%61&3T(( >[(\R_QZSQ(R)Q!SQ()Q(h^Q(-3*-%T( h[\)._)_!Q()!.!)Q(_!#Z^( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # H2B5#T# `e( >Ä[(\#QA^Q\!Q=:WQÅQt^Q!QhÄS( hÄ([(\!TT[(#!=W(Ç(#AW( K5CCSh5+#h5CCShi# hiCCS5i+#5iCCS5K# A=TT[AA( AWTT[A^( ( >[(R\#QA^Q\!Q=:W^Q!QhS( h([(\!TT[(#!=W(Ç(#AW( K5CCS#5K# A=TT[AA( AWTT[A^( ! 43,( &%*/0#H%,(d0%(,3*("%1"%,%*2#-3,(13"(>_(,%( &#*( &%*/0#H%,( ,'*("%,2"'$$'3*%,( ! W+36,yG( Zkck:( E3-3( 4R>_S( 10%-%( ,%"( -%,$"'23( 13"( 0*#( >_( $3*( %,2"0$20"#(-%(B"#,%,:( [R-0G49# !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # H2B5#U# `f( 6S#=!d+#!D+#$+#A>( !d+!D#S!+#%4;%:-<9#37%0jB'%+# !d0!DS#*# >Z( )%*,'A&%,(#&(W3*2%j23( jQG#!vQ(!#!V( O#!m(#(V3(1%"6'2%("%/&#,($361"%,3"#,( 7j$%1$'F*T(R)TT[(%S#h( Q!Y#CCS#Q@Y# 7H%61&3T(( >[(R\#QAQ$^Q(\!Q=^Q!Q(h^Q(( h[\!(TT[(!##(}(#Q(( (((((((#!(TT[(#=(}(#Q(( (((((((#WW$(TT[(#!#W$Q( (((((((W(TT[($^( Los Lenguajes representados por una gramática de Tipo 1 se llaman lenguajes dependientes del contexto o lenguajes sensibles al contexto (se puede cambiar A por v, siempre en el contexto x...y)( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # H2B5#U# `g( 7H%61&3(-%(>(d0%(,'(%,(>Z( 43,( &%*/0#H%,( d0%( ,3*( "%1"%,%*2#-3,( 13"( >Z( ,%( &#*( ,-&3F%R-*#*-&*):4-*#%4#'9&<-Q<9# -3*-%(( %#4R>ZS()''(R)TT[%S#h( 7H%61&3(-%(>(d0%(*3(%,(>Z( >[(R\#QA^Q(\)^Q()Q(hS(Q(( h[(\()TT[(####)AAAAQ((((((((((((((((((((((((((((((((((((((( (#)ATT[(#A^( >[(R\#QA^Q(\)^Q()Q(hS(Q(( h([(\()TT[(####)AAAAQ((((((((((( (#)ATT[(#AA^( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # H2B5#U"#85#E%3.%32/2%&15# `k( A79G)-.%.#.-#DZ#L[KO[K2k2[DdZ#.-#4%*#6J( 4#,( $#-%*#,( d0%( ,%( 3AD%*%*( %*( $0#&d0'%"( -%"'O#$'F*( -%( 0*#( >Z( ,3*( -%( &3*/'20-(*3(-%$"%$'%*2%Q(%,(-%$'"T( #F#.#@#"#(@(,(F(# 4#(&3*/'20-(-%(&#(1#"2%(-%"%$+#(-%(&#(1"3-0$$'F*(%,(6#G3"(3('/0#&(#(&#(&3*/'20-( -%(&#(1#"2%('5d0'%"-#( L-09*<7%')E&# 1!2(.(132(( -3*-%(3#R!E+!VESm(13"(-%L*'$'F*(-%(>Z(R*3($361"%,3"#,S( %,(-%$'"Q(3(4(%(,'%61"%Q(&3(d0%('61&'$#(3(,(Z(( G($363((!([(Z($363(6?*'63Q(d0%-#(-%63,2"#-3( !" #$ %& '( )* +#! 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"#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # J.C56%+#E%#E%.2F)32G&# f_( Forma Sentencial: E.E !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # J.C56%+#E%#E%.2F)32G&# fZ(Sentencia: 1.2 !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # J.C56%+#E%#E%.2F)32G&# K#-#(&#(>([(R\#QA^Q(\!Q)^Q()Q(\)TT[(#!)(}(#Q(!TT[()A!(}( ))(}(A#^S:(U#&&#"(0*(C"A3&(-%(-%"'O#$'F*(1#"#(0*#( ,%*2%*$'#(-%(e(&%2"#,:( ( fJ( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # J.C56%+#E%#E%.2F)32G&# K#-#(&#(>([(R\#QA^Q(\!Q)^Q()Q(\)TT[(#!)(}(#Q(!TT[()A!(}())(}(A#^S:(U#&&#"(0*( C"A3&(-%(-%"'O#$'F*(1#"#(0*#(,%*2%*$'#(-%(e(&%2"#,:( A S A S S a a a ab b A S S S S a a aaaa A S b Sería de 7 letras fP( !" #$ %& '( )* +#! 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( ZZJ( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # 45./)#85./)6#E%#LI5/+S,# a*#(/"#6CD$#(A'%*(B3"6#-#(%,2C(%*(I3"6#(V3"6#&(-%(W+36,yG(RIVWS(,'( &#,( 1#"2%,( -%"%$+#,( -%( 23-#,( ,0,( "%/&#,( -%(1"3-0$$'F*(D%*%*( #( &3( ,063( -3,(,?6A3&3,Q(G($0#*-3(,3*(-3,Q(#6A3,(,3*(V3(E%"6'*#&%,:( [R-0G49C#4#(,'/0'%*2%(/"#6CD$#(%,2C(%*(IVWT( ( ()(TT[(%(}(#(}(VV( ( (V(TT[(VE(}(!=( ( (!(TT#( ( (=TT[(A( ZZP( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # 45./)#85./)6#E%#LI5/+S,# ZZ`( !(1#"D"(-%($0#&d0'%"(/"#6CD$#(-%(E'13(JQ(,%(10%-%($3*,2"0'"( 32"#(%d0'O#&%*2%(d0%(%,2C(%*(IVW:( N292# 7EEA"# 07# 87O7=# 0B0L>B,9# 87E# 0,PB,7=>7# 1A8A# E20# 97PE20# ;B$2# @29>7# 8797;Q2#L7=7#1R0#87#*#0S1OAEA0#@A9#:29,20#97PE20#TB7#>7=P2=#7=#E2#@29>7# 8797;Q2#8A0#0S1OAEA0#=A#>791,=2E70#A#B=#0AEA#0S1OAEA#>791,=2E3# !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # #45./)#85./)6#E%#LI5/+S,# ZZc( A ::= x |x| = 1 !T FNC ( A :: = a ) !N REDENOMINACION ( A :: = B ) u " !N u " !T |v| = 1 y v " !N FNC ( A :: = BC ) |v| > 1 o v"!T A :: = uv A :: = uv |x| > 1 x = uv, donde |u| = 1 A :: = uC FNC ( A ::= BC ) C ::= v A :: = Dv D ::= u FNC ( A ::= a ) C # !N G’ = !N ${C} D # !N G’ = !N $ {D} FORMA NORMAL DE CHOMSKY !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # 45./)#85./)6#E%#LI5/+S,# ZZe( >([((R\#Q(AQ($^Q(\!Q(=Q(WQ(KQ(7Q(I^Q(!Q(hS( h([( =TT[= ( (( WTT[W ( (( !TT[!=W (( KTT[# ( (( 7TT[IA= ( (( ITT[7#! ( (( !TT[A!( =TT[=#( !TT[#=A( =TT[A!#( !TT[#( =TT[#( WTT[$( WTT[WA( [1[kA,ZC# !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # 45./)#85./)6#E%#LI5/+S,# ZZf( >([((R\#Q(AQ($^Q(\!Q(=Q(WQ(KQ(7Q(I^Q(!Q(hS( h([( =TT[=( ($;**%$%,#"'#( WTT[W( ($;**%$%,#"'#( !TT[!=W (( KTT[#( ($;**#$$%,'A&%( 7TT[IA= ( ($;**#$$%,'A&%( ITT[7#! ( ($;**#$$%,'A&%( !TT[A!( =TT[=#( !TT[#=A( =TT[A!#( !TT[#( =TT[#( WTT[$( WTT[WA( Bien Formar la Gramática >"#6CD$#(='%*(I3"6#-#T( >([((R\#Q(AQ($^Q(\!Q(=Q(WQ(KQ(7Q(I^Q(!Q(hS( h([( !TT[#(( !TT[#=A( !TT[!=W( !TT[A!( =TT[#( =TT[=#( =TT[A!#( WTT[$( WTT[WA( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # 45./)#85./)6#E%#LI5/+S,# ZZg( >"#6CD$#(='%*(I3"6#-#T( >([((R\#Q(AQ($^Q(\!Q(=Q(WQ(KQ(7Q(I^Q(!Q(hS( h([( !TT[#( ()?(RIVWS( !TT[#=A ( (V3(RIVWS( !TT[!=W ( (V3( !TT[A! ( (V3( =TT[#( ()?( =TT[=# ( (V3( =TT[A!# ( (V3( WTT[$( ()?( WTT[WA ( (V3( E"#*,B3"6#$'F*(#(IVW(Rd0%-#*(2#A0&#-#,(&#,(*0%O#,( "%/&#,(/%*%"#-#,(%*(IVWS( ( E"#2#6'%*23(-%(!TT[#=A( !TT[#=A( (LCCS%( !TT[K=A( 7TT[=A( (!CCSL[( (fCCS:( #[CCS5f# # ( E"#2#6'%*23(-%(!TT[!=W( !TT[!=W( (6CCS5K( #!CCS!6# # ( E"#2#6'%*23(-%(!TT[A!( !TT[A!( (!CCSf!( E"#2#6'%*23(-%(=TT[=#( =TT[=#( #5CCS5L# ( ( E"#2#6'%*23(-%(=TT[A!#( =TT[A!#( =TT[I!#( UTT[!#( 5CCSfs# sCCS!L# # # E"#2#6'%*23(-%(WTT[WA( WTT[WA( #KCCSKf# !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # #45./)#85./)6#E%#-.%2C)3I# ! FNG es una notación muy interesante para algunos reconocimientos sintácticos. En ella todas las reglas tienen la parte derecha comenzando con un terminal seguido opcionalmente de uno o varios NT ! TEOREMA: todo L de contexto libre sin % puede ser generado por una G2 en la que todas las reglas sean de la forma: • A . a1 donde A #!NT ,a#!T y 1 #!NT* • Si % # L habrá que añadir S::= % ! TEOREMA: toda G2 puede reducirse a otra G2 equivalente sin reglas recursivas a izquierdas ZZk( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # #45./)#85./)6#E%#-.%2C)3I# FNG: para transformar una G2 en su equivalente en forma normal de Greibach: 1. Limpiar y formar bien. Eliminar la recursividad a izquierdas 2. Aplicar el algoritmo de transformación a FNG, verificando en cada paso que no aparezcan nuevas reglas recursivas a izquierdas y si aparecen, eliminándolas con el paso 1 [1[kA,ZC# >([(R\#QA^Q(\)^Q()Q(hSQ(-3*-%(h([(\)TT[#)A(}())(}(%^(( ZJ_( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # #45./)#85./)6#E%#-.%2C)3I# Z: 7&'6'*#"(&#("%$0",'O'-#-(#('5d0'%"-#,Q("%,06'%*-3Q(,%"?#T( ,%#(>([(R\1ZQ(1JQ(2ZQ(2J^Q(\!^Q(!Q(hSQ(( -3*-%(h([(\!TT[(!(1Z}(!1J(}(2Z}(2J^( q0%-#"?#T( A::= 21 | 22 | 21X | 22X X::= 11| 12 |X| 12X 7&'6'*#"(&#("%$0",'O'-#-(#('5d0'%"-#,T( )(TT[(#)A(}( ))(}( %(à R,%(2"#*,B3"6#(%*S(à( )(TT[(#)A(}( #)AÅ(}(%( G(Å(TT[()Å(}( )( ZJZ( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # 45./)#85./)6#E%#-.%2C)3I# J: E"#*,B3"6#$'F*(-%(>J(A'%*(B3"6#-#(,'*(N;(#(IV>T( # M"J([*<%:4-'-7#F&%#7-4%')E&#.-#97.-&#G%7')%4#-&#!Dd# !VE([(\!ZQ(!JQ(:::Q(!*^(A#,C*-3,%(%*T(,'(!'(.(!H(1Q(!'(1"%$%-%"C(#(!H:( W0#*-3( +#G( "%/&#,( X$3*2"#-'$23"'#,Y( 0,#"( 0*#( -%( %&&#,( 1#"#( %&( 3"-%*(G(6'"#"(%&("%,23(1#"#(O%"(d0%($3*O'%*%(6C,( !(TT[(â=ä(R!(,%"?#(*ã(Z(G(=(*ã(JS:(â(%,(0*#($#-%*#(-%(_(3(6C,(2%"6'*#&%,(G( ä(0*#($#-%*#(-%(_(3(6C,(,?6A3&3,:( =(TT[(åWç(R=(,%"?#(*ã(J(G(W(*ã(PS:(å(%,(0*#($#-%*#(-%(_(3(6C,(2%"6'*#&%,(G( ç(0*#($#-%*#(-%(_(3(6C,(,?6A3&3,:( # ZJJ( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # 45./)#85./)6#E%#-.%2C)3I# J: E"#*,B3"6#$'F*(-%(>J(A'%*(B3"6#-#(,'*(N;(#(IV>T( M"M#$-#'4%*)?'%%*#7-34%*#-&#N#37FG9*C# 67FG9#JC#!)#.#%#1(Q-3*-%(#(#!E(G(1(#!(v( 67FG9#MC#!)#.#!R#1(-3*-%(!'(1"%$%-%(#(!H(%*(%&($3*H0*23(!VE(3"-%*#-3( 67FG9#NC#!e#.#!)#1(-3*-%(!'(1"%$%-%(#(!y(%*(%&($3*H0*23(!VE(3"-%*#-3( ( U#$%"(&3(6',63($3*(&#,(-%(/"013(J( M"-%*#"(&3,(*3(2%"6'*#&%,T(\ÅQ()^(G($&#,'L$#"(&#,("%/&#,(,%/b*(%,2%(3"-%*T( )(TT[(#)A(R>ZQ(#0*d0%(+#G(d0%(d0'2#"(%&(2%"6'*#&(d0%(%,2C(-%2"C,(-%&(*3(2%"6'*#&S( )(TT[(#)AÅ(R>ZQ(#0*d0%(+#G(d0%(d0'2#"(%&(2%"6'*#&(d0%(%,2C(-%2"C,(-%&(*3(2%"6'*#&S( )(TT[(%( R>ZS( Å(TT[()Å(R>JS( Å(TT[()(R>JS( ZJP( !" #$ %& '( )* +#! "#, -. -/ 0 %+ #1" #23 4- *) %* +#5 "#6 %7 '8 %+ #1" #! 49 &* 9# # 45./)#85./)6#E%#-.%2C)3I# J: E"#*,B3"6#$'F*(-%(>J(A'%*(B3"6#-#(,'*(N;(#(IV>T( M"N#$-#<7%&*;970%%*#7-34%*#.-#37FG9#N#.#37FG9#M#.#37FG9#JC#fD6# !e#.#!)#1##,%(,0,D20G%(!)(13"(&#(1#"2%(-$+#:(-%(23-#,(&#,("%/&#,(d0%(D%*%*(!)( $363(1#"2%('5-#:( ( U#$%"(&3(6',63($3*(&#,(-%(/"013(J( M"-%*#"(&3,(*3(2%"6'*#&%,T(\ÅQ()^(G($&#,'L$#"(&#,("%/&#,(,%/b*(%,2%(3"-%*T( )(TT[(#)A(R>ZQ(#0*d0%(+#G(d0%(d0'2#"(%&(2%"6'*#&(d0%(%,2C(-%2"C,(-%&(*3(2%"6'*#&S( )(TT[(#)AÅ(R>ZQ(#0*d0%(+#G(d0%(d0'2#"(%&(2%"6'*#&(d0%(%,2C(-%2"C,(-%&(*3(2%"6'*#&S( )(TT[(%( R>ZS( Å(TT[()Å(R>JS( Å(TT[()(R>JS( ZJ`( !" #$ %& '( )* +#! 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