COMP 7612
HOMe Wok-2
Kapako 50mt
2)Gien statement thad,
eth
bs eesy
eveby i y ob eople
fsiends
o
enemies uith
each
hey
othe a t a
e
Ue hoJe
hoLe tto
prst ue
haug
a Bume that
a
atleost
hae
Consides thad eeyore doesit
one enemy
So, il
mut
be tue thal each
iends o
be
he
enemies
Hence, he Qiven
aove
poiy Pople
stotemen
with Cach
stotement
5
ale in the fom
tnend
ierd
mu
othey
Ue
o
y
Conrodichon
Contoluchon
CRA TR)
Blve ord
cosides te 20oy
l e l us
goy pebbks d
amay MXIN
Tepresents
z; b the
let
TOws
represents the
m
50 that
numbey
e n/2
:
the Columns
blUC
o
bbles
in the i
atmos hall
0s in oh Tow
0lo
1he
pebbles
aTe blu
50, a t2t Z3-
ge b e
the
Hence, ,
-
-
tZm
numbes of
blue
mn/2
pebbls
in the
i"clumn
t2t --- +Zn = 4 2
yIty2y3+ - Yn 4 mn2
SuPpse
these
ests
mo
column awlh
Pebbles
moYe
han hall Qa
inicolumn
or blue pebbles
noumbes
S6,
ebbles
numbes o 9ay
i5
=y.
wlumn
50,
m-Hi m 2
Hence
m2
+Jn 2mn2
50
whi
Con
adi cts the
ft---
+ Yn-
Thus,. there euss
u
obll
Osumphem
a.
gly euists
mnl2
Column
in
o
tret alleast
two ierborak
Ob
@
a
b
descsiphon
toimal
hese
as
tbllouws
ur vsf
Vs,
n,
,
f
stals":
ss Anite sitb
f: {a,bj
is Anle sedb p
stant stoleis
Pnad staleiof: V5
d- J5
a
tonsishum
a1gumens
6
únchion
of
mappng
state g inputsymbol
fonchon
Yebns
a
/ fokes
stale
h e qiven Outomcda sepsesents| o cepts he bllouwirq
ShoiO
he sel o shsinq ale={
baabbaab, boaa
boob oa bbaab,
bbaob
bbaabaobhaa.---
stir "baabbo ab"
intal stoeis , t
the
21 considesirq
is d s o the
fsom the
ssinq
dr
then second jeHer
'6,
values
a epts he
(i-e b a e
9,to
tate l
be chaged from
veauns
Je us considey a
ot he
Fe 4hrd letes
uchanged (i.t baa)
it) CFe mezt
h e nert
sbio s d
jeHes s b6o the
leta is "b
stbte
ogain the
so
the stade
(ie boa b)
chages Kom the
stale
charme erm t o y
stade
15 'a' sothe
leH
nert
i n h e the
stale
it adephs the
firal
i s the
bao bbaab)
chaged (ie
un
,toi-ebaobb)
chargy fom to
ebaabba)
ab
so the
stae Temcuns
1
1
1
, 92, Vsj
fo,
s
yo
O
& , ,n, sj
{0.1
Vo/.,ul (9o,9a
Consides the Stolement
A=t 10,
001,
B-
C
Co)
=
oot,
loo, Ocol,
loloo, 11o00,
0lol----g
IIlO000,
Oolool-
-
-
-}
Itoo, llo, llo00, 000111
tooti|u00, 10lo010, 1lo00uM000, 0oloolOcoil--S
1l00 ool, 1/10 tolo0, 1I0001o00,
HLBoc)U(co B)- foou
0001ul
oo lool---J
00, 101001 10, 110001 1iOOo
-
00 001,U1olOlO0,
Au
wokirg
I|ODllo0o
at the stolement A condlition
alltost
al luost 1 0s
By doing
Sel sb
15
the
unon
elemenks
that the
o
contains alleost
ue con
thi eomple
A- (0oc)U(co)
set
-
-
A com fains
15
eb Boc ad CoB
thad
hente by
Dme
00o ||l1oolool-
e
will
9
the
1s arol a l l o t
proof that
the
Gniven Auomoda
eonia Hhe
he aboue auBomao
sirg
tral
erds uih
ab os empy
lab
6 5
b
Ghen Autommta
numes5
he outomota
as g bs
which contans even
accepts Hhe soirg
een Oume dtas
hos atlecd areb ard an
b
ate the last
b
5
S
t
CaTéesian
alomata
produt
{5, 94,
Ys,
1j
b
O
b
5
0-
(E)
(1E)
d g 2