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Tetott a 2 2cooo2lo
AOANa. k
Tetbs
p r e t t e t i a .
some
veqular -Cepreion % ame some
t p l a f n
+be fdenifty ules e1 Ate 7alar
ep Kion Asstme a e C ale vequkay
eeprestong in he denfYiqruDes.
A Teclan Exremion a eqeme
acteu Act deires aeach Patte?n
ette n ued to matoh tois,e
paoto1stsinqs in text dota.
dentfy PuleRtO1 Pegul teprrekion
N u e strs 9
ta,b C aue the Tegula Eepfesiou..
3) e Cec
) C+
6 C c
a t C.c
)(a b *aa lh.a*
u)(atb)t - (a. *) * (attb*)*
C.Catb) c.atd.b
Congder the langtuage tven ythe
egulay ee prenibn Catb)bCath) ovey
alpabet Sa.b Denga a BP-A that
acceps
4he que
s t toe neead Conveott he9Yueg
Ee he
egula rpreton nto n N Ee theo
acceflo
toe need nd out he DF-A tho acelo
Deqsla epression ta4b blatb)
NFA
Transitton Diagram: M (@, ¬,8 ,1
atb
o 1,1?
(a, )
TankitioD Table S o o,F-S=,
sate te-SeconitUct The
Tasle
le take
S
T671 o. 707,22-
o Sg
HeRe Sa, Sy Me he Sirial states.
Dn - tutstia
e Constvuet talole
o de he
aqonhm
to Contet NED to
b
a
S eeaao eepseisn.
, Cro e a
fequlan
EepesBan teh e
Sy
S S -ettouot ne Nf
Sy
hele S3 , Sy ae the
oa tates Arsi thn o Corst
NE-inrto eguay
eepreA ion
a
a
credte a neo
Storte de he tht
9tat e er tta NEA
ereate a neud
4ate t the autceppt state dt The A
he Tansiton in he reo auomaetion,
t q +he ttlowingmules to detekmine
3) Js each Fanaitoo
Tequlaecpresion totanstton
a) Foa raniton fsom State to rtute
&yebol athe Teqala ErprerB
Yon a
feP the trong?tton is a
b) te a transition fom stute t o state
Yon he ermpty KtoingCe) ,the
Tegulan tepresion ft fe transiton g
State o
e)Fe the transYtfon dsom state
Stat e
on the e ef mbes Ca,a
an e
T e g e l a preuion
he
Jnaitt
on a, l la 1a
d) F atansf4ton om state ba
mhe
Seotates , T3 m
oequla e*presmon ie ' 2
Add an Cpilbn tandition rsom the ne
Hat storte tothe eld stast stote,
dd an pailon tanatton om he td
to the neu acce tarte.
an
accept storte
The egala esresson. the nu
tast State A he regalat epreaion
h e otd aceept Stt e
Thrg algonihm uoil eonteslt any NE
tto e a erpresion.
the 9ien NEA is;
a
a
9 , +2,b+2b
om eq'n O
suo og' n eq'nO
(,a+
a tbt9an
Aom eq'n
2 +9,b4 b scao Nalue n
2 at9b+Q,ab
om Arsden'
Theose
, a + Cbab
P
4(20)lbtaby* -)
eq'n
e+2,a sulo egnts) Sn egnti
+4a+{C2,a)tlotab) *b
A 4 Ca t a tbtab)*)b
P
(latalb +ab)*)b
(+a (btob)*)L*)-©
Fal storte (
Lsuoe4n snO
2 a (b+ah)*a ub'n6
( a t a lbtab" bJ* a lotab)*a
Required Pegaln ¾presion
4e
iNen NEA
9) eepain Arden's thetem +o
onve+F9 TO
e he algoRthm to Cenvest the jolloim
DE- o Re
O
dents Theose m:
p e a e oo megeala Cepren
Contaitys E,
ve E t Pdoes, Dot cote e,
henthefoltowing EquaGn dn2
ten
en by PBtRP has a
unque
a uniue
Sotutio)
.eGP
R 8P*
e +PP
P p*
tenee POYed
ottutto)
unige
P+Qt +FPnt
+NP+0p?- Op +Oppn41
e tp+4. p tptpnt
4, oule
Te
Pep$ends
P
This
ond One
untque eluten.
The eD finite Aurtomo
L
4 4t9Ctto1)
P
2
2Litoi
som
o2,0+1(to1*oo te
P
o e Co+ 1 (rtoi)*co)
Lolo+(td) oo
post ut sia
)Pod the equla eeprexion * *he fh
he
ng
b
Thexe exisis muae Ana states , So Loe
Conte+ hem snto atngle finaltete.
etiminate all rtemediate tages 2u,3
ataes
C
d
ets eltmnate
) htctd)
Popla preMibn a
Chttd)
)Fo a, b?,Jet consde
Yegulns
tanquoge
L xlxa242 : 419
ohat ceud be the minim m int'm
Cthe constant anaurdes d b he
pumpin emma) {a L,
Regula Larae
L: a,aS,as.a"..,65
pumng temma
Let lce an
inite equla lamuage.
Toen thee exies ome pesÍ t ne
stega
Sudh 4hat
luolm
be deaopoked as
X 2
Bueh thtt uot X'2 s aluo
L all isO, t,2,.
Minimum pumpìg leth houtd be
becaue sing uoth teath ot e , os 6)
doearet Sepeat any hia
but
-t+n9
ith
tngtn
t
eteuos
")
wul
ep
t
a
t
e
s
es
24
a
n
e
the
pumpia
lemma
enath

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Regular expression to accept a given language

  • 1. Tetott a 2 2cooo2lo AOANa. k Tetbs p r e t t e t i a . some veqular -Cepreion % ame some t p l a f n +be fdenifty ules e1 Ate 7alar ep Kion Asstme a e C ale vequkay eeprestong in he denfYiqruDes. A Teclan Exremion a eqeme acteu Act deires aeach Patte?n ette n ued to matoh tois,e paoto1stsinqs in text dota. dentfy PuleRtO1 Pegul teprrekion N u e strs 9 ta,b C aue the Tegula Eepfesiou.. 3) e Cec ) C+ 6 C c a t C.c )(a b *aa lh.a* u)(atb)t - (a. *) * (attb*)* C.Catb) c.atd.b
  • 2. Congder the langtuage tven ythe egulay ee prenibn Catb)bCath) ovey alpabet Sa.b Denga a BP-A that acceps 4he que s t toe neead Conveott he9Yueg Ee he egula rpreton nto n N Ee theo acceflo toe need nd out he DF-A tho acelo Deqsla epression ta4b blatb) NFA Transitton Diagram: M (@, ¬,8 ,1 atb o 1,1? (a, ) TankitioD Table S o o,F-S=, sate te-SeconitUct The Tasle le take S T671 o. 707,22- o Sg HeRe Sa, Sy Me he Sirial states.
  • 3. Dn - tutstia e Constvuet talole o de he aqonhm to Contet NED to b a S eeaao eepseisn. , Cro e a fequlan EepesBan teh e Sy S S -ettouot ne Nf Sy hele S3 , Sy ae the oa tates Arsi thn o Corst NE-inrto eguay eepreA ion a a credte a neo Storte de he tht 9tat e er tta NEA ereate a neud 4ate t the autceppt state dt The A he Tansiton in he reo auomaetion, t q +he ttlowingmules to detekmine 3) Js each Fanaitoo Tequlaecpresion totanstton a) Foa raniton fsom State to rtute &yebol athe Teqala ErprerB Yon a feP the trong?tton is a b) te a transition fom stute t o state Yon he ermpty KtoingCe) ,the Tegulan tepresion ft fe transiton g
  • 4. State o e)Fe the transYtfon dsom state Stat e on the e ef mbes Ca,a an e T e g e l a preuion he Jnaitt on a, l la 1a d) F atansf4ton om state ba mhe Seotates , T3 m oequla e*presmon ie ' 2 Add an Cpilbn tandition rsom the ne Hat storte tothe eld stast stote, dd an pailon tanatton om he td to the neu acce tarte. an accept storte The egala esresson. the nu tast State A he regalat epreaion h e otd aceept Stt e Thrg algonihm uoil eonteslt any NE tto e a erpresion. the 9ien NEA is; a a 9 , +2,b+2b om eq'n O suo og' n eq'nO
  • 5. (,a+ a tbt9an Aom eq'n 2 +9,b4 b scao Nalue n 2 at9b+Q,ab om Arsden' Theose , a + Cbab P 4(20)lbtaby* -) eq'n e+2,a sulo egnts) Sn egnti +4a+{C2,a)tlotab) *b A 4 Ca t a tbtab)*)b P (latalb +ab)*)b (+a (btob)*)L*)-© Fal storte ( Lsuoe4n snO 2 a (b+ah)*a ub'n6 ( a t a lbtab" bJ* a lotab)*a Required Pegaln ¬æpresion 4e iNen NEA
  • 6. 9) eepain Arden's thetem +o onve+F9 TO e he algoRthm to Cenvest the jolloim DE- o Re O dents Theose m: p e a e oo megeala Cepren Contaitys E, ve E t Pdoes, Dot cote e, henthefoltowing EquaGn dn2 ten en by PBtRP has a unque a uniue Sotutio) .eGP R 8P* e +PP P p* tenee POYed ottutto) unige
  • 7. P+Qt +FPnt +NP+0p?- Op +Oppn41 e tp+4. p tptpnt 4, oule Te Pep$ends P This ond One untque eluten. The eD finite Aurtomo L 4 4t9Ctto1) P 2 2Litoi som
  • 8. o2,0+1(to1*oo te P o e Co+ 1 (rtoi)*co) Lolo+(td) oo post ut sia )Pod the equla eeprexion * *he fh he ng b Thexe exisis muae Ana states , So Loe Conte+ hem snto atngle finaltete. etiminate all rtemediate tages 2u,3 ataes C d ets eltmnate
  • 9. ) htctd) Popla preMibn a Chttd) )Fo a, b?,Jet consde Yegulns tanquoge L xlxa242 : 419 ohat ceud be the minim m int'm Cthe constant anaurdes d b he pumpin emma) {a L, Regula Larae L: a,aS,as.a"..,65 pumng temma Let lce an inite equla lamuage. Toen thee exies ome pesÍ t ne stega Sudh 4hat luolm be deaopoked as X 2 Bueh thtt uot X'2 s aluo L all isO, t,2,. Minimum pumpìg leth houtd be becaue sing uoth teath ot e , os 6) doearet Sepeat any hia