Tema4 UC3M TALF-SANCHIS-LEDEZMA-IGLESIAS-JIMENEZ …

!"#$%&'()*%+#,#-.)/0123)+#45./)6%+#

!"#$%&'()#*$+',(-%(.'/0%&(!/#1'23(4%-%56#(7,1'*3(83,9(!:(;/&%,'#,(.#"<*%5(=%#2"'5(>#"$?#(8'69*%5(80#*(.#*0%&(!&3*,3(@%A%"(

>"#-3(;*/%*'%"?#(;*B3"6CD$#(E%3"?#(-%(!02F6#2#,(G(4%*/0#H%,(I3"6#&%,((

$78-9:;7<#4=>?:$7<# J(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

K%L*'$'3*%,(

M1%"#$'3*%,(

N%/&#,(-%(-%"'O#$'F*(

P(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

@%A2&2325&%+#$80:949#7*D-#-(#A,2"#$2#Q(*3(,%(-%L*%(R#*C&3/3(#&(10*23(%*(/%36%2"?#S:()3*(

&%2"#,Q( -?/'23,Q( $#"#$2%"%,Q( %2$:( E#6A'9*( %,( 13,'A&%( %*$3*2"#"(

,?6A3&3,(B3"6#-3,(13"(O#"'3,($#"#$2%"%,Q(1%HT(;IQ(EU7VQ(74)7Q(:::(

!4;%:-<9#=!>##W3*H0*23(?&)<9#&9#@%'89(-%(&%2"#,(3(,?6A3&3,:(

)%#( X#Y( 0*#( &%2"#( G(!( 0*( #&B#A%23Q( ,'( #( 1%"2%*%$%( #( %,%(

#&B#A%23("(#(#(!(

7H%61&3,T(

!Z[(\!Q(=Q(WQ(:::Q]^(

!J[(\_Q(Z^(

!P[(\;IQ(EU7VQ(74)7Q(=7>;VQ(7VK^(

`(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

@%A2&2325&%+#A%4%:7%+#'%.-&%+#B7%C(23-#(,%$0%*$'#(L*'2#(-%(,?6A3&3,(-%&(#&B#A%23:(

7H%61&3,T(

1#&#A"#,(,3A"%(!Z(8a!VQ(;)!=74Q(%2$:(

1#&#A"#,(,3A"%(!J((___ZZZ_Z(1#&#A"#,(,3A"%(!P(;IEU7V74)77VK((

D9<%')E&C# &#,(1#&#A"#,(,%("%1"%,%*2#*(13"( &%2"#,(6'*b,$0&#,(-%&(L*#&(

-%&(#&B#A%23(

(R!"#$"#%SQ(1%H(![(8a!VQ($[(;IEU7V74)77VK(c(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

@%A2&2325&%+#,9&3)<F.#.-#G%4%:7%#((

7,(%&(*b6%"3(-%(,?6A3&3,(d0%($3613*%*(0*#(1#&#A"#(4#(&3*/'20-(-%(&#(1#&#A"##!#,%("%1"%,%*2#(13"($(!$(7H%61&3,T(

$(!$([($(8a!V#$([(`($($#$([($(;IEU7V74)77VK($([ZP(R%*(!ZS($($#$([($(;IEU7V74)77VK($([((`(R%*(!PS((

A%4%:7%#@%'8%#=%>#((7,(#d0%&&#(1#&#A"#($0G#(&3*/'20-(%,($%"3()%("%1"%,%*2#(13"#%+($(%#$([(_()3A"%($0#&d0'%"(#&B#A%23(%,(13,'A&%($3*,2"0'"(%#HB4).%.C# %,( %&%6%*23( *%02"3( %*( 60$+#,( 31%"#$'3*%,( $3*(1#&#A"#,(G(&%*/0#H%,(

e(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

@%A2&2325&%+#H&)@-7*9# .-4# .)*'F7*9+#I=!>C# ( 7,( %&( $3*H0*23( -%( 23-#,( &#,(1#&#A"#,( d0%( ,%( 10%-%*( B3"6#"( $3*( &3,( ,?6A3&3,( -%( 0*(#&B#A%23(!((

!  E#6A'9*(,%(-%*36'*#(4%*/0#H%(a*'O%",#&(-%(!(

!  )%("%1"%,%*2#($363(@R!S(

!  7,(0*($3*H0*23('*L*'23(

!  7H%61&3T(,%#(!`([(\!^Q(@R!`S([(\%Q(!Q(!!Q(!!!Q(:::^($3*(0*(

*b6%"3(&(-%(1#&#A"#,(

COROLARIO: ' !, % # W(!) " La palabra vacía pertenece a todos los lenguajes

universales de todos los alfabetos posibles f(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

K%L*'$'3*%,(

M1%"#$'3*%,(

N%/&#,(-%(-%"'O#$'F*(

g(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

=B%.)325&%+#35&#B)6)C.)+#M1%"#$'3*%,( $3*( 1#&#A"#,(,3A"%(1#&#A"#,(-%(0*(0*'O%",3(-%&(-',$0",3(-#-3(

Z(

J(

P(

W3*$#2%*#$'F*(-%(1#&#A"#,(

h32%*$'#(

N%i%j'F*(

k(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

J# K9&'%<-&%')E&#.-#G%4%:7%*#

,%#*(-3,(1#&#A"#,(!Q($(2#&(d0%(!#!#&'"(Q(($!!#&'"(Q((G(,%#(((

$(!$([('([(&(!)#!*#+++!,$((%(($$$([(H([($($)#$*#+++#$-($Q((

,%(&&#6#('9&'%<-&%')E&(-%(j($3*(GQ(#T(

!#"#$([(!)#!*#+++#!,(($)#$*#+++#$,(([(#+((-3*-%(%#!#&'"((

Z_(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

A79G)-.%.-*C##!  M1%"#$'F*($%""#-#(R3('*2%"*#S( ( ((

!  h"31'%-#-(!,3$'#DO# ( ((

!  W3*(%&%6%*23(*%02"3:(((

!  V3($3*602#DO#(

J# K9&'%<-&%')E&#.-#G%4%:7%*#

L-?&)')9&-*C##!  W#A%5#(

!  W3&#(

!  43*/'20-(-%(1#&#A"#( ZZ(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

M# A9<-&')%#7,(&#("%-0$$'F*(-%(&#($3*$#2%*#$'F*(#(&3,($#,3,(d0%(,%("%L%"%*(#(0*#(6',6#(1#&#A"#(

!  132%*$'#( ,./0,12# -%( 0*#( 1#&#A"#( #&( "%,0&2#-3( -%( $3*$#2%*#"(%,#(1#&#A"#($3*,'/3(6',6#('(O%$%,(

!  $3*$#2%*#$'F*(%,(#,3$'#DO#("(*3(%,1%$'L$#"(%&(3"-%*((!  j'([(j(l(j(l(j(:(::::j('((O%$%,((!  (j'(([('(l((j(((!  ,%($061&%T(

•  jZ([(j(•  j(Z(m('([(j(l(j'([(j'(l(j((R'n_S(•  j(H(m('([(jH(l(j'([(j'(l(jH((R'Q(Hn_S(

!  )'(,%(-%L*%(j_([(%((•  R'Q(Hn[_S(

ZJ(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

N# O-P-Q)E&#.-#F&%#G%4%:7%#)%#(&#(1#&#A"#(j([(#Z(l#J(l(#P(l:::(l(#*Q(((

(,%(-%*36'*#(G%4%:7%#7-P-R%#-%(jQ((( ((( (joZ([((#*(l#*oZ(l(:::(l(#J(l(#ZQ((( (((B3"6#-#(13"(&3,(6',63,(,?6A3&3,(%*(-',D*23(3"-%*((

(( ((joZ(([((j(((

ZP(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

=B%.)325&%+#35&#6%&'()*%+#

Z`(

':%:((#(23-3($3*H0*23(-%(1#&#A"#,(,3A"%(0*(-%2%"6'*#-3(!((

':%:(#(23-3($3*H0*23(-%(1#&#A"#,((/%*%"#-3(#(1#"D"(-%&(#&B#A%23(!((

(

pq09(%,(0*(4%*/0#H%r((

)%( -%*36'*#( ,-&3F%R-# *9:7-# -4# %4;%:-<9#!( #( 23-3(,0A$3*H0*23(-%&(&%*/0#H%(0*'O%",#&(-%(!(R4()(@R!SS(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

=B%.)325&%+#35&#6%&'()*%+#

Zc(

)3*(&%*/0#H%,(%,1%$'#&%,T(

*([(4%*/0#H%(O#$?3Q(*()(@R!S(

\s^([(4%*/0#H%(-%(&#(1#&#A"#(O#$?#(*( G( \s^( ,%( -'B%"%*$'#*( %*( %&( *b6%"3( -%( 1#&#A"#,(R$#"-'*#&'-#-S(d0%(&3,(B3"6#*(WR*S([(_(6'%*2"#,(d0%(WR\s^S[Z( ,%( 1#"%$%*( %*( d0%( *( G( \s^( ,3*( &%*/0#H%,(,3A"%($0#&d0'%"(#&B#A%23(

a*(#&B#A%23(%,(0*3(-%(&3,(&%*/0#H%,(/%*%"#-3,(13"(%&(6',63T(

!()(@R!SQ((13"(%H%61&3(%&($+'*3(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

=B%.)325&%+#35&#6%&'()*%+#M1%"#$'3*%,( $3*( &%*/0#H%,(,3A"%(0*(0*(#&B#A%23(-#-3(!(

Z(J(P(

a*'F*(-%(&%*/0#H%,(

W3*$#2%*#$'F*(-%(&%*/0#H%,(

='*3'-%(&'A"%(

Ze(

`(c(e(

h32%*$'#(-%(0*(&%*/0#H%(

W&#0,0"#(3($'%""%(13,'DO3(-%(0*(&%*/0#H%(

;2%"#$'F*Q($&#0,0"#(3($'%""%(-%(0*(&%*/0#H%(

f( N%i%j'F*(-%(&%*/0#H%,(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

Zf(

J# H&)E&#.-#4-&3F%R-*#

)%#*(4Z(G(4J(-%L*'-3,(,3A"%(%&(6',63(#&B#A%23(!Q(4ZQ(4J()(@R!SQ((

,%( &&#6#( F&)E&( -%( -3,( &%*/0#H%,Q( 4ZQ( 4J( ( G( ,%( "%1"%,%*2#( 13"( 4Z+( 4J( #&(

&%*/0#H%(#,?(-%L*'-3T(

,J#+#,M#S#T#Q#U#Q###,J#E##Q###,M#V##

7,(%&($3*H0*23(B3"6#-3('*-',D*2#6%*2%(13"(1#&#A"#,((

-%(0*3(0(32"3(-%(&3,(-3,(&%*/0#H%,(R%d0'O#&%(#(&#(,06#S(

(

(,J#W#,M#S#,J#+#,M#

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

Zg(

M# K9&'%<-&%')E&#.-#4-&3F%R-*#)%#*(4Z(G(4J(-%L*'-3,(,3A"%(%&(6',63(#&B#A%23Q(4ZQ(4J()(@R!SQ((

,%(&&#6#('9&'%<-&%')E&#9#G79.F'<9(-%(-3,(&%*/0#H%,Q(4Z(G(4J(Q(G(,%("%1"%,%*2#(

13"(4ZX(4J(#&(&%*/0#H%(#,?(-%L*'-3T((

,J#X#,M##S#T#QY#U#Q###,J##!DL##Y###,M#V#(

!  7,(%&($3*H0*23(-%(1#&#A"#,(B3"6#-3(13"(&#($3*$#2%*#$'F*(-%(1#&#A"#,(-%(4Z(

$3*(1#&#A"#,(-%(4J(!  K%L*'$'F*(OC&'-#(1#"#(&%*/0#H%,($3*(#&/b*(%&%6%*23:(

!  t($3*(%&(&%*/0#H%(O#$?3T(*(l(4([(4(l(*([(*(!  7&(%&%6%*23(*%02"3(%,(\s^T(\s^:4([(4:(\s^([(4(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

Zk(

M# K9&'%<-&%')E&#.-#4-&3F%R-*#

A79G)-.%.-* ((

! (M1%"#$'F*($%""#-# ( ( ( ((

! (h"31'%-#-(!,3$'#DO# ( ((

! (W3*(%&%6%*23(*%02"3(

! (h"31'%-#-(-',2"'A0DO#("%,1%$23(#(&#(0*'F*:(

(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

J_(

N# 5)&9).-#4):7-#

!  4#($3*$#2%*#$'F*(R63*3'-%S(-%(&%*/0#H%,(G(&#(0*'F*(R63*3'-%S( (-%(

&%*/0#H%,($3*,D20G%*(0*(:)&9).-#

!  43,( ,?6A3&3,( -%( !( ,%( 10%-%*( $3*,'-%"#"( $3*H0*23,( -%( 0*#( ,3&#(

1#&#A"#(

!  W3*( !Q( &#( 0*'F*( G( &#( $3*$#2%*#$'F*( ,%( 10%-%( B3"6#"( $0#&d0'%"(

&%*/0#H%(,3A"%(-'$+3(!:(7j$%123((*(G(\%^:(

(

7&(#&B#A%23(!(%,(0*($3*H0*23(-%(/%*%"#-3"%,(1#"#(%&($3*H0*23(

4("(,#-*#-4#52DZ2L[#,25O[#=9G-7%')9&-*#H#Y#">#3-&-7%.9#G97#!#

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

JZ(

\# A9<-&')%#.-#F&#4-&3F%R-#!  7,(&#("%-0$$'F*(-%(&#($3*$#2%*#$'F*(#(&3,($#,3,(d0%(,%("%L%"%*(#(

0*(6',63(&%*/0#H%(!  132%*$'#(,./0,12(-%(0*(&%*/0#H%(#&("%,0&2#-3(-%($3*$#2%*#"(%,%(

&%*/0#H%($3*,'/3(6',63(,(O%$%,#!  $3*$#2%*#$'F*(%,(#,3$'#DO#("(*3(%,1%$'L$#"(%&(3"-%*((!  4'([(4(l(4(l(4(l(:::(l(4((u(((,((O%$%,((!  )%(-%L*%(4Z([(4(!  )%($061&%T(

4(Z(m('([(4(l(4'([(4'(l4(R'n_S(4(H(m(('([(4'(l(4H((R'Q(H(n_S(

!  )'(,%(-%L*%(4_([(\(%(^Q(%*23*$%,(R',_S(R'Q(H(,(_S(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

JJ(

]# K4%F*F7%#9#')-77-#G9*)B@9#)%( "%1"%,%*2#( $363( 4m( (G( %,(%&( &%*/0#H%(

3A2%*'-3( 0*'%*-3( %&( &%*/0#H%( 4( $3*(

23-#,(,0,(132%*$'#,(13,'A&%,(%j$%123(4_(

L+ = Lii=1

!!

Ninguna clausura positiva contiene a %, si %-L

Como ! es un lenguaje sobre !, la clausura positiva de ! será:

!+ = !ii=1

"! =W !( )# !{ }

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

JP(

^# 2<-7%')E&+#'4%F*F7%#9#')-77-#

!  )%($061&%T(

,_#S#,W#H#T%V#,W#S#,_X#,#S#,#X#,_#

!  (W363(!(%,(0*(&%*/0#H%(,3A"%(!Q(,%(&%(10%-%(#1&'$#"(%&(vT(

!_#S#I#=!>#

)%("%1"%,%*2#($363(4v(G(%,(%&( &%*/0#H%(3A2%*'-3( 0*'%*-3( %&( &%*/0#H%( 4( $3*(23-#,(,0,(132%*$'#,(13,'A&%,:((#_#%,(%&(31%"#-3"(0*#"'3(-%(w&%%*%(

!!

==

0ii* LL

E3-#($&#0,0"#($3*D%*%(#(%(

El lenguaje universal es !*

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

J`(

`# O-P-Q)E&#.-#4-&3F%R-#

)%( &&#6#( &%*/0#H%( "%i%H3( 3( '*O%",3( -%( 4( G( ,%(

"%1"%,%*2#(13"(4oZ(#&(&%*/0#H%T(

,aJ#S#TQaJ#b#Q###,V#(%,( -%$'"Q( #&( &%*/0#H%( B3"6#-3( 13"( 23-#,( &#,(

1#&#A"#,("%i%H#,(-%(4(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

K%L*'$'3*%,(

M1%"#$'3*%,(

N%/&#,(-%(-%"'O#$'F*(

Jc(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

D.5E(3325&%+#

Je(

)%#(!(0*(#&B#A%23(

!  )%(&&#6#(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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

->:?JHKL:<#4=>?:$7<# PJ(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

K%L*'$'3*%,(

8%"#"d0?#(-%(W+36,yG(

z"A3&%,(-%(-%"'O#$'F*(

PP(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

$%&'()*%#)+532)E5#)#(&)#'.)/0123)#

`Z(

)%#(&#(/"#6CD$#T((>Z([(R!EQ(!VQ()Q(hS(

()%(&&#6#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"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

>%3(.+2F2E)E#

`J(

)%#(H"#!  a*#(H(,%(&&#6#(7-'F7*)@%#-&#0Q(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"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

K%L*'$'3*%,(

8%"#"d0?#(-%(W+36,yG(

z"A3&%,(-%(-%"'O#$'F*(

`P(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"(>_(,%( &&#6#*( &%*/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"#234-*)%*+#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"#234-*)%*+#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( ,%( &&#6#*(,-&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"#234-*)%*+#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(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

H2B5#V#

c_(

G= (!T, !N, S, P)(!T+!N =!, alfabeto gramjtica,

!T0!N= *

G2 De Contexto Libre

O#!v(!#!V(

!#CCS#@#

7H%61&3T((>[(R\_QZQJQPQ`QcQeQfQgQk^Q\VQK^Q)Q(hS(h[\V(.(KV(}(KQ((((((((K(.(_(}(Z(}(J(}(P(}(`(}(c(}(e(}(f(}(g(}(k^(

(R$CCS#%>##A#G(R!CCS#%>#-A#((R#&/3"'263(&'61'%5#("%/&#,(VM(/%*%"#DO#,S(

"( #( h( ,%( $#"#$2%"'5#*( 13"(2%*%"(0*(,F&3(,?6A3&3(VE(%*(,0(1#"2%('5d0'%"-#(

K9&<-Q<9#,):7-C#)%(10%-%($#6A'#"(!(13"(@Q(%*($0#&d0'%"($3*2%j23((

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

H2B5#V#

cZ(

)'(%((#(4R>JS:#(

43,( &%*/0#H%,( d0%( ,3*( "%1"%,%*2#-3,( 13"(>J( ,%(&&#6#*(,-&3F%R-*#&9#*-&*):4-*#%4# '9&<-Q<9#9#.-#'9&<-Q<9#4):7-#

'(4R>JS(/(4R>JÄS(,'*("%/&#,(!TT[(%(R!(4()S(

10%-%(#1&'$#",%(%&(#&/3"'263(-%(%&'6'*#$'F*("%/&#,(VM(/%*%"#DO#,:( !"

#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

H2B5#W#

cJ(

6S#=!d+#!D+#$+#A>(!d+!D#S!+#%4;%:-<9#37%0jB'%+#

!d0!DS#*#

>P(>"#6CD$#,(N%/0&#"%,(

6N#,)&-%4-*#G97#4%#2/.%"(!CCS#%#!CCS#l#%($CCS#%(

6N#,)&-%4-*#G97#4%#L7'(%"(!CCS#%#!CCS#%#l($CCS#%(

#(#(!E(!Q~(#(!V(()(%,(#j'36#(

"(#( h( 0*( ,F&3( ,?6A3&3(VE( %*(,0(1#"2%( '5-#(G( ,0(1#"2%(-$+#($36'%*5#(13"( 0*( E( ,%/0'-3(3(*3( -%( VE( R#&( "%O9,( %*( &'*%#&(-%"%$+#S(

7H%61&3T(>[(\R#QASQ(R)Q!SQ)Q(h^Q((h[\R)(.(#)Q()(.(#!Q(!.(A!Q(!(.(AS^(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

H2B5#W#

cP(

43,(&%*/0#H%,(d0%(,3*("%1"%,%*2#-3,(13"(>P(,%(&&#6#*(4-&3F%R-*#7-3F4%7-*#

'  4R>PS(/(4R>PÄS(,'*("%/&#,(!TT[(%(R!(4()S(((

)'(%(#4R>PS:((

~%"(#&/3"'263(%&'6'*#$'F*("%/&#,(VM(/%*%"#DO#,:( !"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

;%.).Q(R)#E%#LI5/+S,"#>%+(/%&#

c`(

6N#,)&-%4-*#G97#4%#2/.%"(!CCS#%#!CCS#l#%($CCS#%(

6N#,)&-%4-*#G97#4%#L7'(%"(!CCS#%#!CCS#%#l($CCS#%(

##!E(!Q~#!V((

6m"#D9#O-*<7)&3).%*#9#'9&#[*<7F'<F7%#.-#f7%*-( 6J"#$-&*):4-*#%4#K9&<-Q<9(

6M"#L-#K9&<-Q<9#,):7-( 6N"#67%0jB'%*#O-3F4%7-*(

O(#(!v(!(#(!V(

!#CCS#@#

jQ(G(#!vQ(!#!V((O#!m(#(V3(1%"6'2%("%/&#,('90G7-*97%*#7j$%1$'F*T(R$CCS#%>#A(

Q!Y#CCS#Q@Y(0#!m(O#!v(

F#CCS#@(((�*'$#("%,2"'$$'F*T(%CCS#@#-A#

6N#)#6M##)#6J#)#6m#

K9&#[*<7F'<F7%#L-#f7%*-*C(Rj!GTT[jOGS(#(hQ(-3*-%T(jQ(G(#(!v(Q(!(#(!VQ(O#!v()'((O[%(#((j!G(TT[(jG("%/&#,($361"%,3"#,(

(R$CCS#%>##A#G(R!CCS#%>#-A#(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#%Q(2F)6%&1%+#

cc(

K#-#( 0*#( /"#6CD$#( &'*%#&( 13"( &#( -%"%$+#( $0#&d0'%"#Q(

%j',2%( 32"#( &'*%#&( 13"( &#( '5d0'%"-#( %d0'O#&%*2%( G(

O'$%O%",#:(

K3,( /"#6CD$#,( ,3*( %d0'O#&%*2%,( ,'( "%1"%,%*2#*( %&(

6',63(&%*/0#H%:(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#%Q(2F)6%&1%+#

ce(

!4>MN;E.MT(P(h!)M):(

h!)M(Z:(

W3*,2"0'"(0*#(/"#6CD$#(%d0'O#&%*2%(d0%(*3(,%#("%$0",'O#(%*(%&(#j'36#T(

Z:  ,%(#É#-%(0*(*0%O3(,?6A3&3(%*(%&(#&B#A%23(!VQ(=(

J:  '()TT[(jQ(-3*-%(j#!mQ(,%(#É#-%(0*#("%/&#(=TT[(j(

P:  )%(2"#*,B3"6#*(&#,("%/&#,(!TT[(#()(Rd0%(-%,#1#"%$%*S(%*("%/&#,(-%&(

D13(!TT[(#(=:(

`:  4#,("%/&#,(D13()TT[(%(*3(,%(O%*(#B%$2#-#,(13"(%,2%(#&/3"'263:#

Nota: las reglas S ::= x, x # !+, no desaparecen

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#%Q(2F)6%&1%+#

cf(


h!)M(Z:(

W3*,2"0'"(0*#(/"#6CD$#(%d0'O#&%*2%(d0%(*3(,%#("%$0",'O#(%*(%&(#j'36#T(

>Z([(R\#QA^Q(\)Q(!^Q()Q((h^((h([($(()(TT[(A!Q(

(!(TT[(#)((}(#(^(

>J([(R\#QA^Q($Q(!Q(=^Q()Q((h^((h([(\((()(TT[(A!Q(

(!(TT[(#=((}(#(((=(TT[(A!^(

h!)M(Z(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#%Q(2F)6%&1%+#

cg(


h!)M(J:(

W3*,2"0$$'F*(-%(0*(/"#B3(-'"'/'-3(#(1#"D"(-%(&#(/"#6CD$#:((#S(*b6%"3(-%(*3-3,([(WR!VS(mZQ($#-#(*3-3(%Dd0%2#-3($3*(,?6A3&3,(-%(!V(G(32"3($3*(%(

(AS($#-#(!TT[#(=(#h((($S($#-#(!TT[#(#h(((-S(,'()TT[(%(#h((

(

A B a

A %

S %

a

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#%Q(2F)6%&1%+#

ck(


h!)M(J:(

W3*,2"0$$'F*(-%(0*(/"#B3(-'"'/'-3(#(1#"D"(-%(&#(/"#6CD$#.

>J([(R\#QA^Q(\)Q(!Q(=^Q()Q((h^((h([(\((()(TT[(A!Q(

(!(TT[(#=((}(#(((=(TT[(A!^(

1#,3(J(S A

% B

b

a b

a

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

(d7%&*;970%')E&#.-4#37%;9#.)7)3).9#%&<-7)97C#

#S  '*2%"$#6A'#"(%Dd0%2#,(-%()(G(%(

AS  '*O%"D"(,%*D-3(-%(23-3,(#"$3,(

$S  -%,+#$%"(%&($#6'*3(G(/%*%"#"(&#,(*0%O#,("%/&#,((

"( '*2%"1"%2#"( %&( /"#B3( 1#"#( 3A2%*%"( &#( >P4;(

%d0'O#&%*2%((

-.)/0123)+#%Q(2F)6%&1%+#

e_(

A B a

% A

% S S::= %


h!)M(P:(

)%('*2%"$#6A'#*(&#,(%Dd0%2#,(G(,%($3*,2"0G%(0*(*0%O3(/"#B3:(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#%Q(2F)6%&1%+#

eZ(


h!)M(P:(

)%('*2%"$#6A'#*(&#,(%Dd0%2#,(G(,%($3*,2"0G%(0*(*0%O3(/"#B3:(

h!)M(P(

)( !(

%( =(

A(

#(A(

#(

% A

B

b

a b

a

S !"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#%Q(2F)6%&1%+#

eJ(


!(1#"D"(-%&(/"#B3Q(,%(3AD%*%(&#(/"#6CD$#(%d0'O#&%*2%(#('5d0'%"-#,:(

%( !(

=(

A(

#(A(

#(

)(

>P([(R\#QA^Q(\)Q(!Q(=^Q()Q((h^((h([(\((()(TT[(!#Q(

(!(TT[(=A((}(A(((=(TT[(!#^(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#%Q(2F)6%&1%+#

eP(


W361"3A%63,(d0%(&#,(/"#6CD$#,(,3*(%d0'O#&%*2%,:::(

>Z([(R\#QA^Q(\)Q(!^Q()Q((h^((h([($(()(TT[(A!Q(

(!(TT[(#)((}(#(^(

>P([(R\#QA^Q($Q(!Q(=^Q()Q((h^((h([(\((()(TT[(!#Q(

(!(TT[(=A((}(A(((=(TT[(!#^(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

K%L*'$'3*%,(

8%"#"d0?#(-%(W+36,yG(

z"A3&%,(-%(-%"'O#$'F*(

e`(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

J.C56%+#E%#E%.2F)32G&#

!  !(&#,(-%"'O#$'3*%,(-%( &#,(H#L@A#)"#*#$#M# &%,($3""%,13*-%(0*(C"A3&(-%(-%"'O#$'F*(%d0'O#&%*2%Q(2#6A'9*(&&#6#-3(((

nj7:94#*)&<j'B'9o#E##nG%7*-#<7--o#

!  N%1"%,%*2#(&#,(1"3-0$$'3*%,(#1&'$#-#,(-0"#*2%(&#(/%*%"#$'F*((-%(F&%#*-&<-&')%Q(%,(-%$'"Q(,0(%,2"0$20"#(-%(#$0%"-3($3*(&#(>(

ec(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

J.C56%+#E%#E%.2F)32G&#

7,(0*(C"A3&(6%,&$(,6(G(&78/&9(,6(d0%(,%($3*,2"0G%T(

!  4#("#?5(,%(-%*32#(13"(%&(#j'36#(-%(>(R)(+#A'20#&6%*2%S(

!  a*#( .-7)@%')E&# .)7-'<%# ,%( "%1"%,%*2#( 13"( 0*( $3*H0*23( -%(%(:(;!8/&!;('&$!,&!/$!$6,6!,(,6!<=(%9&!*#8/*&%,(!,&!'(!>?!

!  !1&'$#"(0*#("%/&#(0*(,?6A3&3(-%(&#(1#"2%('5d:(d0%-#(,0,D20'-3(13"( 0*#( 1#&#A"#( B( -%( &#( 1#"2%( -$+#:( h3"( $#-#( 0*3( -%( &3,(,?6A3&3,( -%( B( ,%( -'A0H#( 0*#( "#6#( d0%( ,#&%( -%&( VE( #( %,%(,?6A3&3T(

ee(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

J.C56%+#E%#E%.2F)32G&#

ef(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

J.C56%+#E%#E%.2F)32G&#7*(0*#(>ZQ(#-%6C,Q(,%(-%A%($3*,%"O#"(%&($3*2%j23:(h#"#($#-#("#6#T(

!  %&(*3-3(-%(1#"D-#(,%(&&#6#(G%.7-(-%&(*3-3(L*#&(

!  %&(*3-3(L*#&(%,(()R9(-%&(*3-3(1#-"%(

!  -3,(*3-3,(+'H3,(-%&(6',63(1#-"%(,%(&&#6#*((-70%&9*(

!  0*(*3-3(%,(%*'-&.)-&<-( -%(32"3( ,'( %,( ,0(1#-"%(3(#,$%*-'%*2%(-%( ,0(

1#-"%(

!  0*(*3-3(%,(.-*'-&.)-&<-(-%(32"3(,'(%,(,0(+'H3(3(-%,$%*-'%*2%(-%(,0,(

+'H3,(

eg(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

J.C56%+#E%#E%.2F)32G&#!  !( &3( &#"/3(-%&(1"3$%,3(-%($3*,2"0$$'F*(-%&(C"A3&Q( &3,(*3-3,(L*#&%,(

-%( $#-#( 1#,3( ,0$%,'O3Q( &%?-3,( -%( '5d-#:( #( -$+#:( -#*( &#( @6%:(!

;&$9&$)*('!3A2%*'-#(13"(&#(-%"'O#$'F*("%1"%,%*2#-#(13"(%&(C"A3&:(

!  7&()6$A/$96!,&! '(;!.6A(;!,&'!B%C6'! R*3-3,(-%*32#-3,(13"(,?6A3&3,(

2%"6'*#&%,( 3( %S( &%?-3,( -%( '5d-#:( #( -$+#:( *3,( -#*( &#( ;&$9&$)*(!

/%*%"#-#(13"(&#(-%"'O#$'F*(

ek(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

J.C56%+#E%#E%.2F)32G&#

f_(

Forma Sentencial:

E.E

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

J.C56%+#E%#E%.2F)32G&#

fZ(Sentencia: 1.2

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#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"#234-*)%*+#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(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

J.C56%+#E%#E%.2F)32G&#K#-#(&#(>([(R\_QZQJQPQ`QcQeQfQgQk^Q(\VQW^Q(VQ(\V(TT[(VW(}(WQ(W(TT[(_}Z}J}P}`}

c}e}f}g}k^S:(U#&&#"(0*(C"A3&(-%(-%"'O#$'F*(1#"#(V(.(JPc(

N

N C

N

2

C

C

3 5f`(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

J.C56%+#E%#E%.2F)32G&#K#-#(&#(>([(R\_QZ^Q(\!Q=^Q(!Q(\!TT[(Z!(}(M=Q(=TT[(_=(}(_^S(0*#(-%($0G#,(-%"'O#$'3*%,(

OC&'-#,(%,T(!(.(Z!(.(ZM=(.(Z__=(.(Z___:((U#&&#"(0*(C"A3&(-%(-%"'O#$'F*(1#"#(!(

.(Z___(

A

B

A

1

B

0 0 0 fc(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

<(C0.C56%+#E%#E%.2F)32G&#Dado un árbol A correspondiente a una

derivación, se llama subárbol de A al

árbol

!  cuya raíz es un nodo cualquiera de A,

!  c u y o s n o d o s s o n t o d o s l o s

descendientes

de la raíz del subárbol en A

!  y cuyas ramas son todas las que unen

dichos nodos entre si en A.

A

B

A

1

B

0 0 0

subárbol

fe(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

<(C0.C56%+#E%#E%.2F)32G&#d-97-0%(

4#,( +3H#,( -%( 0*( ,0AC"A3&Q( &%?-#,( -%( '5-#:( #( -$+#:Q( B3"6#*(

0*#(B"#,%("%,1%$23(#&(,?6A3&3(VE("#?5(-%&(,0AC"A3&(

A

S A

S

S

a a a ab b

abba es una frase de la forma sentencial aabbaa respecto del símbolo A

ff(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

:/C2'X%E)E#

!  W3*$%123("%&#$'3*#-3($3*(%&(-%(C"A3&(-%(-%"'O#$'F*T(

!  )'(0*#(,%*2%*$'#(10%-%(3A2%*%",%(%*(0*#(>(13"(6%-'3(-%(-3,(3(6C,(C"A3&%,(-%(-%"'O#$'F*(-'B%"%*2%,Q( 4%#*-&<-&')%#-*#%0:)3F%#

!  a*#(6( %,( %0:)3F%( ,'( $3*D%*%( %4#0-&9*# F&%# *-&<-&')%#%0:)3F%#

(

fg(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

:/C2'X%E)E#[Q)*<-&#N#&)@-4-*#.-#%0:)3p-.%.C#

!  D&$9&$)*(C(0*#(,%*2%*$'#(%,(#6A'/0#(,'(10%-%(

3A2%*%",%(13"(6%-'3(-%(-3,(3(6C,(C"A3&%,(

-%(-%"'O#$'F*(-'B%"%*2%,(

((((((((((((((((((%HT(>([(R\Z^Q(\!Q=^Q(!Q(\!TT[(Z=(}(ZZQ(=TT[(Z^S(

!  E%(:B7)(3(%,(#6A'/0#(,'($3*D%*%(#&(6%*3,(0*#(

,%*2%*$'#(#6A'/0#Q(%HT(&#(>(#*2%"'3"(

!  F&$G/(A&!*$.&%&$9&:&$9&!(:C*G/6C(,'(23-#,(&#,(

/"#6CD$#,(d0%(&3(/%*%"#*(,3*(#6A'/0#:(

A

1

B

1

A

1 1

fk(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

:/C2'X%E)E#!  !0*d0%(0*#(>(,%#(#6A'/0#Q(%,(13,'A&%(d0%(%&(&%*/0#H%(d0%(-%,$"'A%(*3(

,%#(#6A'/03( ÑI&3G-(ZkeJ]("( ( %,(13,'A&%(%*$3*2"#"(0*#(>(%d0'O#&%*2%(

d0%(*3(&3(,%#(

!  7j',2%*( &%*/0#H%,(1#"#( &3,(d0%(VM(%,(13,'A&%(%*$3*2"#"(>(*3(#6A'/0#,(

"(4%*/0#H%,(;*+%"%*2%6%*2%(!6A'/03,(Ñ>"3,,(Zke`]((

!  4#( 1"31'%-#-( -%( #6A'/Ö%-#-( %,( '*-%$'-'A&%:( E#*( ,3&3( %,( 13,'A&%(

%*$3*2"#"( $3*-'$'3*%,( ,0L$'%*2%,( d0%( #,%/0"%*( d0%( 0*#( >( %,( *3(

#6A'/0#((

!  2&.-').):4-T(*3(%j',2%(0*(#&/3"'263(d0%(#$%12%(0*#(>(G(-%2%"6'*%($3*(

$%"2%5#(G(%*(0*(D%613(L*'23(,'(0*#(>(%,(#6A'/0#(3(*3:( g_(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

:/C2'X%E)E#,-&3F%R-*# 2&(-7-&<-0-&<-# !0:)3F9*C( 1#"#( &3,( d0%( VM( %,( 13,'A&%(

%*$3*2"#"(>(*3(#6A'/0#,(

[R-0G49((

4([(\\#*A6$6-*^+\#*A*$6-6^(Ç(6Q*,Z^(

(

[R-0G49((

4([(\ZZ^(VM(%,('*+%"%*2%6%*2%(#6A'/03((

>([(R\Z^Q(\!Q=^Q(!Q(\!TT[(Z=(Ç(ZZQ(=TT[(Z^S((

>Ä([(R\Z^Q(\!^Q(!Q(\!TT[ZZ^S((oon(>"#6CD$#(VM(#6A'/0#(

4R>S[4R>ÄS(( gZ(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

:/C2'X%E)E#

K#-#(&#(>([(R\#QA^Q(\!Q=Q)^Q()Q(hS(h([(\(

()TT[(A!(}(#=((!TT[(A!!(}(#(}(#)((=(TT[(A(}=)(}(#==^(

-%63,2"#"( d0%( %,( 0*#( >( #6A'/0#( #&( ,%"&3( &#( ,%*2%*$'#(X%%::%:Y(

gJ(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

:/C2'X%E)E#K#-#(&#(>([(R\#QA^Q(\!Q=Q)^Q()Q(hS(

h([(\(()TT[(A!(}(#=Q(!TT[(A!!(}(#(}(#)Q(=(TT[(A(}(=)(}(#==^(

-%63,2"#"(d0%(%,(0*#(>(#6A'/0#(#&(,%"&3(&#(,%*2%*$'#(X%%::%:Y(

B

B B

S

a a

B S

A

b b a b

B

B

S

B

S

B

a a b b a b gP(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

->:?JHKL:<#4=>?:$7<#)%/0*-#(1#"2%(

g`(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

>"#6CD$#,(E'13(J(

>"#6CD$#,(A'%*(B3"6#-#,(

I3"6#,(*3"6#&%,(

gc(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#K&E%B%&E2%&1%+#E%6#L5&1%Y15#

)3*(&#,(/"#6CD$#,(-%(D13(J(%*(&#(H%"#"d0?#(-%(W+36,yG:((

O-4-@%&')%#

!  ,3*( &#,( %61&%#-#,( %*( &#( K%L*'$'F*( -%( 4%*/0#H%,( -%(

h"3/"#6#$'F*(G(%*(&#($361'&#$'F*(-%(&3,(6',63,(

((

/%*%"#-3"(-%($F-'/3(.(E"#-0$23"(W361'&#-3"(

#*#&'5#-3"(.(#$%12#-3"(-%(&#(>(%j1&3"#-3"(R!IS(

"%$3*3$%-3"(R!hS(

ge(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#K&E%B%&E2%&1%+#E%6#L5&1%Y15#

!( &3,( &%*/0#H%,( /%*%"#-3,( 13"( /"#6CD$#,( -%&( D13( J( -%( &#(

H%"#"d0?#( -%( W+36,yG( ,%( &%,( -%*36'*#( ,-&3F%R-*#

)&.-G-&.)-&<-*#.-4#'9&<-Q<9#9#4-&3F%R-*#.-#'9&<-Q<9#4):7-#

!  )%("%1"%,%*2#*($363(4R>JS(

!  7j',2%*(#&/3"'263,(d0%(1%"6'2%*("%$3*3$%"((

,'(0*(4R>JS(%,(O#$?3Q(L*'23(3('*L*'23(

gf(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#K&E%B%&E2%&1%+#E%6#L5&1%Y15#K#-#(0*#(>Q(%&(4%*/0#H%(d0%(/%*%"#Q(p%,(O#$?3(3(*3rT(

)%#(6MQ(6([(WR!VESQ(,=6M>#4#*( ,'(/(j(#(4R>JS(2#&(d0%(j(10%-%(/%*%"#",%($3*(0*(C"A3&(-%(-%"'O#$'F*(%*(%&(d0%(23-3,(&3,($#6'*3,(D%*%*(&3*/'20-(5(6(

)%( /%*%"#*( 23-3,( &3,( C"A3&%,( -%( -%"'O#$'F*( $3*( $#6'*3,( 5( 6( [( WR!VES( 6%-'#*2%( %&(#&/3"'263T(

#:  $3*H0*23(-%(C"A3&%,($3*(&3*/'20-(_(R0*(C"A3&($3*()($363("#?5(G(,'*("#6#,S(

A:  #(1#"D"(-%&($3*H0*23(-%(C"A3&%,(-%(&3*/'20-(*Q(/%*%"#63,(%&($3*H0*23(-%((&3*/'20-(*mZ(|(6(mZ(#1&'$#*-3(#&( $3*H0*23(-%(1#"D-#(0*#(1"3-0$$'F*(d0%(*3(+#/#(-01&'$#",%(#&/b*(VE(%*(%&($#6'*3($3*,'-%"#-3(

$:  ,%(#1&'$#(%&(1#,3(AS("%$0",'O#6%*2%(+#,2#(d0%(*3(10%-#*(/%*%"#",%(6C,(C"A3&%,($3*($#6'*3,(-%( &3*/'20-(5(6:(!&(,%"(6(G(%&(*b6%"3(-%("%/&#,(-%(h(L*'23("(%&(#&/3"'263(2%"6'*#(

(,=6M>#S#*#*)#&)&3F&9#.-#49*#j7:94-*#3-&-7%#F&%#*-&<-&')%#gg(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#K&E%B%&E2%&1%+#E%6#L5&1%Y15#7H%61&3(-%(4R>JS([(*#

)%#(>([(R\#QA^Q(\!Q=QWQ)^Q()Q(hS(((h([(\(( ()(TT[(#=(}(#!(( (!(TT[(=(}(#A=(( (=(TT[(AW^(

0SK=!Dd>#S#\#

Z:  6[_($#

P:  6[J(

$# $#

#( 5# !##(

$# $#

#( 5# !##(

$#

!##(

5#A( A(#( 5#K#No se generan sentencias y salen NT ya obtenidos Lenguaje vacío

J:  6[Z(

`:  6[P(gk(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#K&E%B%&E2%&1%+#E%6#L5&1%Y15#)'(4R>JS(%,(*3(O#$?3Q($361"3A#"(,'(,=6M>#S#&##

!  )%( $3*,2"0G%( 0*( /"#B3( $0G3,( *3-3,( %,2C*( %Dd0%2#-3,( $3*( &3,(,?6A3&3,(-%(R!VES(6%-'#*2%(%&(#&/3"'263T((#S  ,'(/(0*#(1"3-0$$'F*(!TT[(1(=(2Q(,%($"%#(0*(#"$3(-%(!(#(=(

-3*-%(!Q=(#(!VE(G(1Q2(#(!v((AS  ,'(*3(%j',2%*($'$&3,(%*(%&(/"#B3(%&(4R>JS([(L*'23($S  4R>JS([(&(,'(%j',2%*($'$&3,(#$$%,'A&%,(-%,-%(%&(#j'36#(d0%(

$3""%,13*-%*( #( -%"'O#$'3*%,( -%( &#( B3"6#( !(.m( 1( !( 2Q(-3*-%(}1}m(}2}(n_(Rd0%(*3(,%#*(%(&#,(-3,(#(&#(O%5S:(

(((,=6M>#4#&#*)#&9#(%Y#')'49*#-&#-4#37%;9(

k_(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#K&E%B%&E2%&1%+#E%6#L5&1%Y15#

7H%61&3(-%(,=6M>#S(&#)%#(>([(R\#QAQ$^Q(\!Q=QWQ)^Q()Q(hS(((h([(\(( ()(TT[(#=(Ç(#!(( (!(TT[(#A=(( (=(TT[(AW(Ç(#!(( (W(TT[($(^(

)(

W(

!(

=( 4('*L*'23(

kZ(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

>"#6CD$#,(E'13(J(

>"#6CD$#,(A'%*(B3"6#-#,(

I3"6#,(*3"6#&%,(

kJ(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#Z2%&#45./)E)+#

kP(

E"#*,B3"6#$'F*( -%( 0*#( >( -#-#( %*( 32"#( %d0'O#&%*2%( $0G#,( "%/&#,( -%(

1"3-0$$'F*(%,29*(%*(0*(B3"6#23($#"%*2%(-%('61%"B%$$'3*%,T(

J"   ,)0G)-/%#.-#67%0jB'%*(

%" #N%/&#,(;**%$%,#"'#,(

:" #)?6A3&3,(;*#$$%,'A&%,(

'" #N%/&#,()019"i0#,(

M"   [4)0)&%')E&#.-#*80:949*#&9#3-&-7%B@9*(

N"   [4)0)&%')E&#.-#7-34%*#&9#3-&-7%B@%*(

\"   [4)0)&%')E&#.-#7-34%*#.-#7-.-&90)&%')E&(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

E"#*,B3"6#$'F*( -%( 0*#( >( -#-#( %*( 32"#( %d0'O#&%*2%( $0G#,( "%/&#,( -%(

1"3-0$$'F*(%,29*(%*(0*(B3"6#23($#"%*2%(-%('61%"B%$$'3*%,T(

J"   ,)0G)-/%#.-#67%0jB'%*(

%" #N%/&#,(;**%$%,#"'#,(

:" #)?6A3&3,(;*#$$%,'A&%,(

'" #N%/&#,()019"i0#,(

M"   [4)0)&%')E&#.-#*80:949*#&9#3-&-7%B@9*(

N"   [4)0)&%')E&#.-#7-34%*#&9#3-&-7%B@%*(

\"   [4)0)&%')E&#.-#7-34%*#.-#7-.-&90)&%')E&(

-.)/0123)+#Z2%&#45./)E)+#

>"#6CD

$#(

4'61'#(

>"#6CD

$#(

N%-0

$'-#(

>"#6

CD$#(='%*(I3"6

#-#(

k`(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#Z2%&#45./)E)+#J"   ,)0G)-/%#.-#67%0jB'%*(

%"   O-34%*#2&&-'-*%7)%*T(&#,("%/&#,(!CCS#!##A(,3*('**%$%,#"'#,(G(+#$%*(d0%(>(,%#(

#6A'/0#("(%&'6'*#"&#,((

kc(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#Z2%&#45./)E)+#J"   ,)0G)-/%#.-#67%0jB'%*(

:"   $80:949*# 2&%''-*):4-*C# ,%#(aTT[( j(#hQ( -3*-%(a#!V(4( )( ( G( *3( #1#"%$%( %*( &#(

1#"2%( ( -%"%$+#( -%( *'*/0*#( 32"#( "%/&#( -%( 1"3-0$$'F*Q( ,%( -'$%( d0%( a( %,(

'*#$$%,'A&%:((

E3-3(,?6A3&3(a#!V(*3('*#$$%,'A&%(-%A%($061&'"()(v.(jaG:(

H'*:*$()*+$!,&!;I:C6'6;!*$())&;*C'&;4!

Z:  U#$%"(0*#(&',2#($3*(23-3,(&3,(,?6A3&3,(-%(&#(/"#6CD$#(RE(G(VES(

J:  .#"$#"(%&(#j'36#(-%(&#(/"#6CD$#:(

P:  K#-3( !I$# 334# !B$(#( .#"$#"( 23-3,( &3,( ,?6A3&3,( d0%( #1#"%$%*( %*( &#(

$#-%*#(B(-%(&#(1#"2%(-%"%$+#:(

`:  )'(%*(%&(1#,3(#*2%"'3"(,%(+#(6#"$#-3(#&/b*(,?6A3&3Q(,%("%1'2%(-%(*0%O3(

-'$+3(1#,3(2%*'%*-3(%*($0%*2#(&3,(,?6A3&3,(6#"$#-3,:(7*($#,3($3*2"#"'3Q(

L*(-%&(#&/3"'263:(

(

ke(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

`: (\#Q(AQ($Q()Q(!Q(=Q(W^(((c: (\#Q(AQ($Q()Q(!Q(=Q(W^(e: (\#Q(AQ($Q()Q(!Q(=Q(W^(

Z:  \#Q(AQ($Q()Q(!Q(=Q(W^((P: (\#Q(AQ($Q()Q(!Q(=Q(W^(

-.)/0123)+#Z2%&#45./)E)+#J"   ,)0G)-/%#.-#67%0jB'%*(

:"   $80:949*#2&%''-*):4-*#

[R-0G49((

,%#(&#(>([(R\#Q(AQ($^Q(\)Q!Q=QW^Q()Q(hSQ((

-3*-%(h([(\)TT[(#!(

(!(TT[(=$(

(=TT[(A!(

(WTT[($^((

)'*($#6A'3,:(I'*(#&/3"'263(

K#-*#F&#*80:949#2D!KK[$25,[qq#

J: (\#Q(AQ($Q()Q(!Q(=Q(W^(

kf(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#Z2%&#45./)E)+#J"   ,)0G)-/%#.-#67%0jB'%*(

'"   O-34%*#$FG-7PF%*T(,3*(#d0%&&#,(d0%(*3($3*2"'A0G%*(#( &#( B3"6#$'F*(

-%(1#&#A"#,(j(#!Ev:(((

( (7,2#,("%/&#,($3*D%*%(#&/b*(*80:949#D9#d-70)&%4#&9#3-&-7%B@9:(

E3-3(,?6A3&3(*3(,01%"i03(-%A%($061&'"(a(m.2Q(2#&(d0%(2(#!Ev(

(

!4397)<09#R%,(0*(#&/3"'263("%$0",'O3(-%(6#"$#-3S(

#:  6#"$#"( &3,(VE( 1#"#( &3,( d0%( %j',2%( 0*#( "%/&#(a( TT[( j( -3*-%( j(#!v( R%,( 0*#(

$#-%*#(-%(E(3(%Q(3(%*(1#,#-#,(,0$%,'O#,($3*D%*%(VE(6#"$#-3,S(

A:  ,'(23-3,(&3,(VE(%,2C*(6#"$#-3,("(*3(%j',2%*(,?6A3&3,(,01%"i03,(G(L*(

$:  ,'(&#(b&D6#(O%5(d0%(,%(1#,F(13"(%&((1#,3(#S(,%(6#"$F(0*(VEQ(O3&O%"(#&(1#,3(#S:(

-:  23-3(!(#!VE(*3(6#"$#-3(%,(,01%"i03:( kg(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

#-.)/0123)+#Z2%&#45./)E)+#J"   ,)0G)-/%#.-#67%0jB'%*(

'" #O-34%*#$FGr7PF%*T((%H%61&3T(,%#(>[(R\%QB^Q(\)Q!Q=QWQK^Q()Q(hS(-3*-%(h[(\()TT[(=%(!TT[(!%(}%(

=TT[(W%(}(!B(WTT[(WB(KTT[(B^(

ZÜ(1#,#-#T(

KTT[(B(G(!TT[(%(

L#

!JÜ(1#,#-#T(

=TT[(!B(

$

5

PÜ(1#,#-#T(

)TT[(=%(

7,(0*#($#-%*#((-%(E%"6'*#&%,(

43,(V3E%"6'*#&%,(%,2C*(6#"$#-3,:(

kk(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

#-.)/0123)+#Z2%&#45./)E)+#J"   ,)0G)-/%#.-#67%0jB'%*(

'" #O-34%*#$FGr7PF%*T((%H%61&3T(,%#(>[(R\%QB^Q(\)Q!Q=QWQK^Q()Q(hS(-3*-%(h[(\()TT[(=%(!TT[(!%(}%(

=TT[(W%(}(!B(WTT[(WB(KTT[(B^(

ZÜ(1#,#-#T(

KTT[(B(G(!TT[(%(

L#

!JÜ(1#,#-#T(

=TT[(!B(

$

5

PÜ(1#,#-#T(

)TT[(=%(

(

()'*(6#"$#"T(WQ(d0%(,%(%&'6'*#Q(#,?($363(,0,("%/&#,(

Z__(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

E"#*,B3"6#$'F*( -%( 0*#( >( -#-#( %*( 32"#( %d0'O#&%*2%( $0G#,( "%/&#,( -%(

1"3-0$$'F*(%,29*(%*(0*(B3"6#23($#"%*2%(-%('61%"B%$$'3*%,T(

J"   ,)0G)-/%#.-#67%0jB'%*(

%" #N%/&#,(;**%$%,#"'#,(

:" #)?6A3&3,(;*#$$%,'A&%,(

'" #N%/&#,()019"i0#,(

M"   [4)0)&%')E&#.-#*80:949*#&9#3-&-7%B@9*(

N"   [4)0)&%')E&#.-#7-34%*#&9#3-&-7%B@%*(

\"   [4)0)&%')E&#.-#7-34%*#.-#7-.-&90)&%')E&(

-.)/0123)+#Z2%&#45./)E)+#

>"#6CD

$#(

4'61'#(

>"#6CD

$#(

N%-0

$'-#(

>"#6

CD$#(='%*(I3"6

#-#(

Z_Z(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#Z2%&#45./)E)+#

M"   [4)0)&%')E&#.-#*80:949*#&9#3-&-7%B@9*C##

()%#(>J([(R!EQ(!VQ()Q(hSQ(('!#!D($3*,2"0'"%63,(&#(/"#6CD$#(

>R!SQ(-3*-%(!(%,(%&(#j'36#:()'(,=6=!>>S#*#"(!#-*#*80:949#

&9# 3-&-7%B@9( G( ,%( 10%-%( %&'6'*#"Q( #,?( $363( 23-#,( &#,(

"%/&#,( d0%( &3( $3*2%*/#*Q( 3A2%*'9*-3,%( 32"#( >J(

%d0'O#&%*2%:(

(

Z_J(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#Z2%&#45./)E)+#N"   [4)0)&%')E&#.-#7-34%*#&9#3-&-7%B@%*C#(,3*(!TT[(%(R!4)S(

!4397)<09C#

Z:  7&'6'*#"(-%(&#(>"#6CD$#(&#,("%/&#(-%(&#(B3"6#(aTT[(%(

J:  h3"( $#-#( "%/&#( -%( &#( /"#6CD$#( -3*-%( a( #1#"%5$#( %*( &#(

1#"2%( -$+#:Q( ~TT[jaGQ( ,%( #É#-%( &#( "%/&#( ~TT[jG( R#( 6%*3,(

d0%(G#(%j',2%S:(

P:  N%1%D"(J:(+#,2#(d0%(*3(d0%-%(*'*/0*#("%/&#(-%( &#( B3"6#(

aTT[(%Q(3(d0%(,F&3(d0%-%()TT[(%:( Z_P(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

N"   [4)0)&%')E&#.-#7-34%*#&9#3-&-7%B@%*C#(,3*(!TT[(%(R!4)S(

7H%61&3T(

>([(R\#Q(A^Q(\)Q(hQ(q^Q()Q(h"S(

h"([(\()(TT[(hq(}(#)A(}(h(

(((((h(TT[(#hq(}(#(

(((((q(TT[(qA(}(%(^(

(

[,2k2D!O,!#

-.)/0123)+#Z2%&#45./)E)+#

Regla NO generativa: Q ::= %

Z_`(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

N"   [4)0)&%')E&#.-#7-34%*#&9#3-&-7%B@%*C#(,3*(!TT[(%(R!4)S(

7H%61&3T(

>([(R\#Q(A^Q(\)Q(hQ(q^Q()Q(h"S(

h"([($)(TT[(hq(}(#)A(}(h(

(((((h(TT[(#hq(}(#(

(((((q(TT[(qA(}(%(^(

(

-.)/0123)+#Z2%&#45./)E)+#

>Ä([(R\#Q(A^Q($Q(hQ(q^Q()Q(h"S(

h"([(\()(TT[(hq(}(#)A(}(h(

(((((h(TT[(#hq(}(#(}(#h(

(((((q(TT[(qA(}(A(^(

7&'6'*#"(&#(N%/&#(V3(/%*%"#DO#(

Z_c(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

E"#*,B3"6#$'F*( -%( 0*#( >( -#-#( %*( 32"#( %d0'O#&%*2%( $0G#,( "%/&#,( -%(

1"3-0$$'F*(%,29*(%*(0*(B3"6#23($#"%*2%(-%('61%"B%$$'3*%,T(

J"   ,)0G)-/%#.-#67%0jB'%*(

%" #N%/&#,(;**%$%,#"'#,(

:" #)?6A3&3,(;*#$$%,'A&%,(

'" #N%/&#,()019"i0#,(

M"   [4)0)&%')E&#.-#*80:949*#&9#3-&-7%B@9*(

N"   [4)0)&%')E&#.-#7-34%*#&9#3-&-7%B@%*(

\"   [4)0)&%')E&#.-#7-34%*#.-#7-.-&90)&%')E&(

-.)/0123)+#Z2%&#45./)E)+#

>"#6CD

$#(

4'61'#(

>"#6CD

$#(

N%-0

$'-#(

>"#6

CD$#(='%*(I3"6

#-#(

Z_e(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

#-.)/0123)+#Z2%&#45./)E)+#\"   [4)0)&%')E&#.-#7-34%*#.-#7-.-&90)&%')E&C# (,3*("%/&#,(-%&(D13(!TT[=(

R-3*-%(!(á(=S(

!4397)<09#

Z:  7&'6'*#"(-%(&#(>"#6CD$#(&#,("%/&#(-%(&#(B3"6#(aTT[(~(

J:  h3"( $#-#( "%/&#( -%( &#( B3"6#( ~TT[jQ( #É#-'"( aTT[j( R,'( V3(

7j',2%S:(

P:  N%1%D"( J:( +#,2#( d0%( *3( d0%-%( *'*/0*#( "%/&#( -%(

"%-%*36'*#$'F*:(Z_f(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#Z2%&#45./)E)+#\"   [4)0)&%')E&#.-#7-34%*#.-#7-.-&90)&%')E&C#(,3*("%/&#,(-%&(D13(!TT[=(

R-3*-%(!(á(=S(((7H%61&3T((((>([(R\#Q(A^Q(\)Q(hQ(q^Q()Q(h"S((((h"([(\()(TT[(hq(}(#)A(}(h(

(h(TT[(#hq(}(#h(}(#(

q(TT[(qA(}(A(^(

(

[,2k2D!O,!#

N%/&#(-%(N%-%*36'*#$'F*T(

)(TT[(h(

Z_g(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

-.)/0123)+#Z2%&#45./)E)+#\"   [4)0)&%')E&#.-#7-34%*#.-#7-.-&90)&%')E&C#(,3*("%/&#,(-%&(D13(!TT[=(

R-3*-%(!(á(=S(((7H%61&3T((((>([(R\#Q(A^Q(\)Q(hQ(q^Q()Q(h"S((((h"([($)(TT[(hq(}(#)A(}(h(

(h(TT[(#hq(}(#h(}(#(

q(TT[(qA(}(A(^(

(

>Ä([(R\#Q(A^Q($Q(hQ(q^Q()Q(h"S(

h"([(\()(TT[(hq(}(#)A(}(h(}(#hq(}(#h(}(#(

(((((h(TT[(#hq(}(#(}(#(

(((((q(TT[(qA(}(A(^(7&'6'*#"(&#(N%-%*36'*#$'F*(

Z_k(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

E"#*,B3"6#$'F*( -%( 0*#( >( -#-#( %*( 32"#( %d0'O#&%*2%( $0G#,( "%/&#,( -%(

1"3-0$$'F*(%,29*(%*(0*(B3"6#23($#"%*2%(-%('61%"B%$$'3*%,T(

J"   ,)0G)-/%#.-#67%0jB'%*(

%" #N%/&#,(;**%$%,#"'#,(

:" #)?6A3&3,(;*#$$%,'A&%,(

'" #N%/&#,()019"i0#,(

M"   [4)0)&%')E&#.-#*80:949*#&9#3-&-7%B@9*(

N"   [4)0)&%')E&#.-#7-34%*#&9#3-&-7%B@%*(

\"   [4)0)&%')E&#.-#7-34%*#.-#7-.-&90)&%')E&(

-.)/0123)+#Z2%&#45./)E)+#

>"#6CD

$#(

4'61'#(

>"#6CD

$#(

N%-0

$'-#(

>"#6

CD$#(='%*(I3"6

#-#(

ZZ_(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

>"#6CD$#,(E'13(J(

>"#6CD$#,(A'%*(B3"6#-#,(

I3"6#,(*3"6#&%,(

ZZZ(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

45./)+#85./)6%+#

! )3*(*32#$'3*%,(d0%(,%(#1&'$#*(#(&#,(>JT(

!B%$2#*(#(&#(B3"6#(-%(&#,("%/&#,(-%(1"3-0$$'F*(

! )3*(-3,(&#,(d0%(,%(O#(#(%,20-'#"T(

J6%:(!K6%:('!,&!L.6:;M3!

J6%:(!K6%:('!,&!E%&*C().!

( ZZJ(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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"#234-*)%*+#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%*)?'%&#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"#234-*)%*+#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#$-#<7%&*;970%&#4%*#7-34%*#.-#37FG9#N#.#37FG9#M#.#37FG9#JC#fD6#!e#.#!)#1##,%(,0,D20G%(!)(13"(&#(1#"2%(-$+#:(-%(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`(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#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#$-#<7%&*;970%&#4%*#7-34%*#.-#37FG9#N#.#37FG9#M#.#37FG9#JC#fD6#!e#.#!)#1# #,%(,0,D20G%(!)(13"(&#(1#"2%(-$+#:(-%(23-#,(&#,("%/&#,(d0%(D%*%*(!)(

$363(1#"2%('5-#:(7,(-%$'"Q()0,D20'"(%&(1"'6%"(,?6A3&3(VE(-%(&#(1#"2%(-$+#:(-%($#-#("%/&#(-%&(/"013(P(13"(&#,(1#"2%,(-$+#,:(-%(23-#,(&#,("%/&#,(R%*($0#&d0'%"(/"013S(-3*-%(-'$+3(1"'6%"(,?6A3&3( #1#"%5$#( $363( 1#"2%( '5d0'%"-#:( U#$%"( %,23( +#,2#( d0%( +#G#63,($3*,%/0'-3(d0%(23-#,( &#,( "%/&#,(-%&(/"013(P(+#G#*(,'-3(2"#*,B3"6#-#,(%*("%/&#,(-%( 32"3,( /"013,:( )'( %*( %,2%( 1"3$%,3( #1#"%$%*( "%/&#,( "%$0",'O#,( #( '5d0'%"-#,Q(2"#*,B3"6#"&#,:((U#$%"(&3(6',63($3*(&#,(-%(/"013(J(

ZJc(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#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#$-#<7%&*;970%&#4%*#7-34%*#.-#37FG9#N#.#37FG9#M#.#37FG9#JC#fD6#!e#.#!)#1# #,%(,0,D20G%(!)(13"(&#(1#"2%(-$+#:(-%(23-#,(&#,("%/&#,(d0%(D%*%*(!)(

$363(1#"2%('5-#:(U#$%"(&3(6',63($3*(&#,(-%(/"013(J(

E"#*,B3"6#63,(&#,(-%(/"013(>J(%*(/"013(>ZT(Å(TT[()Å( (à)(TT[(#)Aà( Å(TT[(#)AÅ(R>ZQ(#0*d0%(+#G(d0%(d0'2#"(%&(2%"6'*#&(d0%((

( ( ( ( (%,2C(-%2"C,(-%&(*3(2%"6'*#&S(( (à)(TT[(#)AÅà (Å(TT[(#)AÅÅ(R>ZQ(#0*d0%(+#G(d0%(d0'2#"(%&(2%"6'*#&( ( (( ( (d0%(%,2C(-%2"C,(-%&(*3(2%"6'*#&S(

Å(TT[()( (à)(TT[(#)Aà (Å(TT[(#)A(R>ZQ(#0*d0%(+#G(d0%(d0'2#"(%&(2%"6'*#&(d0%((( ( ( ( (%,2C(-%2"C,(-%&(*3(2%"6'*#&S(( (à)(TT[(#)AÅà( Å(TT[(#)AÅ(R>ZQ(#0*d0%(+#G(d0%(d0'2#"(%&( 2%"6'*#&( ( (( ( (d0%(%,2C( (-%2"C,(-%&(*3(2%"6'*#&S( ZJe(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#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"#\"#W0#*-3(23-#,( &#,("%/&#,(,3*(-%(/"013(ZQ( &#(>(%,2C(%*(IV>(#(B#&2#(-%(

-4)0)&%7# 49*# *80:949*# <-70)&%4-*#&9#*)<F%.9*#-&# 4%#'%:-'-7%#.-# 4%#G%7<-#

.-7-'(%"#

!#.#1##%#2###.9&.-#%#!d#Y#1#4#%((

(

(

7,( -%$'"Q( 2"#*,B3"6#"( &3,( ,?6A3&3,( 2%"6'*#&%,( *3( ,'20#-3,( %*( $#A%5#( -%(

1#"2%(-%"%$+#Q(#,'/*C*-3&%,(*0%O3,(VE(d0%(-%"'O%*(%*(%&&3,(R3(VE(d0%(G#(

%j',2%*(d0%(,F&3(-%"'O%*(%*(%&&3,S:(

!#.#1##5#2#5#.#%#

ZJf(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#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"#\"#W0#*-3(23-#,( &#,("%/&#,(,3*(-%(/"013(ZQ( &#(>(%,2C(%*(IV>(#(B#&2#(-%(

-4)0)&%7# 49*# *80:949*# <-70)&%4-*#&9#*)<F%.9*#-&# 4%#'%:-'-7%#.-# 4%#G%7<-#

.-7-'(%"#

!#.#1##%#2###.9&.-#%#!d#Y#1#4#%((

(

(!#.#1##5#2#5#.#%#

;*2"3-0$'63,(0*(*0%O3(,?6A3&3(1#"#(d0'2#"(%&(AT((5#CCS#:# ZJg(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

45./)#85./)6#E%#-.%2C)3I#

4#(>"#6CD$#(%*(IV>(d0%-#T(((>Ä([(R\#QA^Q(\)QÅQ=^)Q(hÄ^S(((hÄ([($( ()(TT[(#)=(}( #)=Å(}( %(( (Å(TT[(#)=Å(}( #)=ÅÅ( }( #)=(( (=(TT[(A(((((((((^(

>([(R\#QA^Q($^Q()Q(hSQ(((h([(\)TT[#)A(}())(}(%^((

HNHO>FP!

ZJk(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

Z2C625'.)AR)#•  4'A"3(=C,'$3(Z(='A&'3/"#é#(R!!.S:(7*"'d0%(!&B3*,%$#(W0A%"3Q(.#*0%&(!&B3*,%$#(W0A%"3Q(N3A%"23(.3"'GF*()#&36F*:(E%3"?#(-%(#02F6#2#,(G(&%*/0#H%,(B3"6#&%,:(.$>"#xoU'&&(RJ__fS:((W#1?20&3(c(

•  4'A"3(=C,'$3(J(='A&'3/"#é#(RU.aS:(83+*(7:(U31$"3èQ(N#H%%O(.32x#*'Q(8%ê"%G(K:a&&6#*: (;*2"3-0$$'F*(#(&#(2%3"?#(-%(#02F6#2#,Q(&%*/0#H%,(G($36102#$'F*(RPÜ(%-'$'F*S:(7-Q(h%#",3*(!--',3*(@%,&%G:(

•  4'A"3(=C,'$3(`(='A&'3/"#é#(R!!.S:(.#*0%&(!&B3*,%$#Q(80,23()#*$+3Q(.'/0%&(.#"<*%5(M"/#:(E%3"?#(-%(&%*/0#H%,Q(/"#6CD$#,(G(#02F6#2#,:(h0A&'$#$'3*%,(N:!:7:W:(Zkkf(W#1?20&3(P( ZP_(

!"#$%&

'()*+#!

"#,-.

-/0%+#1"#234-*)%*+#5

"#6%7'8%+#1"#!49&*9##

Tema4 UC3M TALF-SANCHIS-LEDEZMA-IGLESIAS-JIMENEZ …

Documents

Transcript of Tema4 UC3M TALF-SANCHIS-LEDEZMA-IGLESIAS-JIMENEZ …