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uie
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mach do,
Inl11Q
Iluii d6m! lllaeh
Cltd
kho,i
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li!le:
\(~~i
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, '
~
L,
• L
gia Iri
1:
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mach
tHong
lrng
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glei
In
O.
Theo
c,i.ch
quy
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gi,i trj
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ph~p
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e6
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dl\':n
nhu
doall m,lch tn.ie
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,~()ng
cae
ki1O,[,
trong khi
d6
ph~p
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h()i
~e
tu'o'ng ling \'6'i
dO,lll
Ille.tell
mill' nt)i
ti(p
dc
kho,i.
Vl'"1i
«ic
qlly
Ul'"1C
d6. tien
d~
hai ella dai
~6
Boo]
C()
the:
dUne
bi~u
chcn thitnh
dc
me.tch
wong
dunng nilu "au:
aT
b.
c
(a+b),(a'
cJ
IIlnh .2.2
SCi
rl()
mach
dtlllg !lgal
1ll111h
hoa
dlO
linn
chXI ph:1Il plHil
S~r
tuong
dU'ung
gili'<l
hai
sO'
do
lmwh khmi
nilY
co
th~
duqc
kicl11
c!ll'rllg h,ing
cac h,ing chan
I)'
tuong ung.
Dl!<l
\,:\0
~~r
tlro'ug thlch
giCi'a
dc
bieu Ihuc
iClgie
\'01
dc
S0
(1<)
mach
khmi
ta
co
Ihe
t'.IO
ra
dc
m',lch khoa
tuong
duong
de
hiel!
thCre
\()glC
\'t1'i
nhlt'llg
dC)
rhll'c qlp kh,\c nhall dl/a
\"ilO
c[te
pher
hl(':'n
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trong m,.tcll
di~n,
I\-'lac
lItl
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eo
m()t
so
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m'.leh kh(mg the
hi~u
dicn
dU"l,K
1!J;l11h
h,'t
hop
giCi'<l
de
t()
h(.ip
mach
~()ng
song
\'il
n6i li':p, troog nhu'ng
tIlJ'i'.ing
hnp
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la ph,ii
x{ry
dtfll~
mach
dl,fa
theo
h,ing ch,tn
Iy
hm~e
su
dt.mg
pi1Llnng
rhiip
li.IO
t')\1
h(,1P
c[ic h('ll
kel.
Chllllg ta xci tnro-ng h0P m',lch
theo
lien
kcI
lll'll'h
crill:
de
(tLfl1!lg
(1i
Ill'
ph:in
phia
Ir,ii
111<,leh
"ang pilfin phla phiil
11l'.leh
bao g()1l1
uic
dtrong
(ab,
aed.
ecb. cd
\.Phll'(mg rh{tp
t'.IO
t~\P
hop
de
lien
ke't
the hi¢n nhu' "au: nell Ircn
bilt
e d
IIlnh
2.3
/l.t<1(11
du.
1<5'
du'o-og
di
IiI'
pll<i,n
ben
Ir[ii
maeh
du
, ,<log
philO
ben ph'l!
ta
dClng
I{II
cit
de
kho,i, kill
do
mach dien se U trall" thai
MJll!.!
ebn
.•
.
~
L'
trang
tru'o-ng
Iwp trcn
moi
duo'ng
C('l
it
nhAt
I11Qt
khOii
111(1
thl
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s0
l1
t .
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th,-ii
mil'.
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ne'u trcn
ducil1g
(lcd ta dt'lllg
1:\1
c:t
de
khOii
a, c, d
m~lCh
se
d
tr~\llg
thai dl'lng.
Nhu
\'~\y
d6i \'6i
nli,leh
Irtn,
bieu
thCl'e
IClgic
tLfO'llg
c1uong
~C
Ia:
21
a.b+a.e
.d+c.e.
h+c.d
Khi
SlJ'
dl.m,!!
1~'
lhuy0'l chuyc'n mach Irong
hieL!
dien
die
hi~u
thClC
iClgic,
de
dinh
15'
ella
d, \i
,,6
chlly~n
mi tell
C()
th~
rut ra
ilf
elc
lien
de.
nguyen
\)'
d6i
ng:hl
etla
I)'
thuyc'\
mach
uj
\'<li
\r()
kllti quail
In~ng.
]\;<ru\'t'n
1\'
dlii
11(l~u:
JEW)'ell
1<'
d6i
ngilU
dua
Ircll cu
w'5
X[tV
dIm"
uk
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•
'"'
L •
L.
.,
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bi~u
thCre
d6i
ng'\u.
D{)i
llg:1ll
eLla
llH)1
bi2u
th{t'c
di.1i
s6
Bool
1:1
IlH)t
hi2u lIllIe
](\gic
lrong
d6
de
b16n
u elta bic'u
thli'C
ban (Ull
duqc
thay
him,!!
(/"."J' lhay bimg
'(r,
'(i'
thay hllllg
'I'.
ph':p
tuy01l
chroe
lhay
btlllg
phcp
Il()!,
phcp
h(ll
lhH/C
Ihay
him,!!
pllcp
tuyen. Kill
th~l!lh
hlp bicll
thCre
d6i ngilu la
piJ.'ti
su'
dung
de
d:iu
ngo(1C
de
d.ltn
IXlO
Irat
II!
tinh
1O
in bieu
there.
Nguyen
15'
dui
ng{\ll:
gi;i
Lrj
eLla
1l1l)t
hieu
111l1-c
(h.1l
s6 Bool
bllllg
bll
ella gia
Ir!
bbieu
thlic doi ng,\u Wong
u'ng.
Ta
e6
lh~
chung
minh
nguyen
I)'
dCii
ngtIU
htlllg plu(o'ng phiip
quy
m,lp
tmin
hqc
va
Sli
ch;Jllg
cae
djnh
I)'
de
Morgan.
1.
('{u:
h:'U11
Wgic \:1 khlii
n-chieu
HilIl1
16gie
/I
bi~ll
throe djnh
nghTa
la anI! xa k.h6ng gian I/-cl!icu
B"
\'ao
II:
B"
>
II
il={O,l)
(2.16)
t<cu
x;
li\ phun Itt Ihu9C
B.
khi do
x=(x/"",xI/J
Iii
m91
\'ccto ella kh6ng gian
veeto'
/I
chicu
nil. Hum
logic
trell kh6ng gian n"
({j
Ihe duqe viet
dU'{l'j
dang
.J(r/
r"J.
KhCmg
gian veeto'
un
eh(ra
2/1
diem
\'a
m(lt
yceW
x Ihu(K kh6ng
glan
B"
chtQ'e
hieu
di~n
iii mot trang
s6
2"
diem
clla kh6ng gian 1/
ehi~ll
nil.
C{IC
diem
nay
e6
the'
dUQ'e
d~lt
{ltong
(rng
\'oi cae dinh
eua
llH)t
hlnh
kh6i
e6
2"
dinh trong kh6ng
gian
B".
HilIll
logie.!L\·/ .
x,,.!
SC
ct~lt
tuang
ling m6i dinh
clla
hlnh
kh6i
\'(.'~i
cae gia trj
()
hO(lc
I.
22
rrong
llu11
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I111e'l
k~
clie
m'.Kh
~6
khllllg
nhil't
thle-L
ph' lI
cli,ll
~)_I' l
Ln
()
ho:)c J
eho
1:11
e<t
Cite
dinh ella khoi -
dIe
\"l'elO' x.
i\NI
dch
ehillh
de
IHin.
1121111
\(lglcj"dude
djnh
Ill:!hTa
Ul
,Inh).a eua t(tp
con
A
cLla
kh(lllg
t'lan
B"
\'ito
B.
r A
c;;
13"
+
B B={O,l)
(.~.17)
Khi la
x01
m(lt
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con
Ac
Bn
\;1
kim
f
ct'l
l111en
x,le dill!.
1;1
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IhU(lC
W
\,;1
kh6ng thu(lc A l
XE
un \ A }
121
lilllh ta kh0ng quail
1~1111
L6i
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h.~,
hi~u
121
l/inh-d;
Cite
dinh Ihu()e
,\
d.
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ling
\'('jl
de
gi<,i
Ifi
()
ho:1C
J
se JlIrrc gqi Ian
IUCft
lit
i/illlr-O
\,,\
d//lII-I. Vdi
Ciich
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UIC
dlllh
ella
hinh
kh6i
2"
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nhu'
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X'.I
de
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/().J.d)·
I(x)
:
il"->
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dinh ella hinh kh6i II-ehieu bi':u
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thCre
I(ltlie.
la
nh(\I1
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nn)1
bi':u
thCre
h()i.
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dl,l
trong khong gian 3-ehicll. dinh
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i
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I
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phfin
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bi~u
Ihlk
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La
cllra
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1;\
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III.
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I)
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(Olx)-kh6ieiip
I:
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nl~'m
I.fili'j
EI
h'lng qual h6a
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klHii
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diuh
eua
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//I
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kh6i cnn
III
ehlcLI
co ch(ra
2'"
lImh. Vi
d\1
kh6i
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(O/())
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(OJ
j).
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rn
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ling
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1/-111
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link
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e6 th':
nh:111
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nell ghi x, khi
gl;1
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ella
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i
1;1
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tqa d() d6
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l kh(lIlg clune
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ky
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bic'n
.
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()
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\'6i dinh
cluy
nh{11
cua
kll6i II-ehicu, kh6i
dip
11/
,'it:
biel!
elien
2'"
dinh,
nhlr
\'[IY
m()1
khoi
dp
til
sc
bao
pill!
2'"
kh6i
b[lC
o.
M{)I
dch
16ng
quat.
v6i hai !flp
I1qp
cae khoi C
I
V~\
C
2
•
nc'u
I~p
hQ'p
dinh
0,\0
phll
1116i
kh6i Ihu(lc nhom
('
I
1~1
1(lp
con ella
ItlP
hop
!.tinh
hao phll
de
kh6i
eLla
C
2
,
khi d6
[a
nOI
r;'mg
C
2
bao phu C
I
•
2.
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d~ng
chU<ln
tile
eua
ham
16gic
T\'cu
h;\111
i(lgie.l
khLing
ehCra
ll/o/l-d, khi do
dC:'
xae dinh ham la
din
dlra
ra
I<)p
h(.~p
de
d/II/I-I
V;'I
dilllr-O.
Do
kh6ng
ehu:a
cal' d/llh-d
ncn
1(lp
hop
dc
d/nh-I(\
"l{))
Y~I
!(Ip
hl)"P
dc
d/nh-O
(Vi!))
htl
nhau.
\'1(11
dinh
("
(kh6i
cAp
())
!Lru"llg
CfIlg
y(ri
m()t bieu
[hCre
hOI
F(cj.
khi
d6
h:ll11
.f(x)
sc
dU(iC
hi~u
(hen
lh6ng
qua
I(lp hop
de
dr'IIIi-1
\!
/f)
nhtl"
-;au:
H\)
= V
Pic)
(2.19)
P(c)
gqi
la
bi~u
thCre
h(li
ct.rc
tieu hay ng{m gqll
l~\
tfeh
eLfc
lieu.
Nlur
[r~n
oJ.
de
c)p
1(1i,
m()[
kh6i
eAp
m
d~\i
di~n
eho
2'"
dinh.
hiju
thCl"e
h(li
ct.re
li(:u
: i:
luang
(rng \'6i
-;6
Iwmg cuc li2u
de
dillh Iham gia
\,;)0
hi~u
Ih(rc h(li
V~I
st::
nh,}n
gi,i
Iri
1
1'.Ii
nhil'ng dinh
nay.
Ricu
thCre
(2.19)
IiI
hieu thu:c
tuyen
ella
de
hieu
Ihue
h(li
eve [iell
\"a
c!Lrq'e
gQi
Ja
d' mg
ehu,ln I,k luycn ella
hi0u
Ih(rc
logic.
Ta x5e dinh
hi:tnl
hCI
I(lgie (
goi
t<"11
I~I
ha111
Otl
)eu<l
m(l[
ham f
I~I
m(ll
hi:lln
nh,:111
gi<.l
Iri
'()'
1<.li
nhung dillli
1l1~1
f nhtlll gi,i
Ir!
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Y;I
nh,-}n
gia lri
'J'
I'.li
nl11.1ng
dinh
lll~lfllh,}n
gi5 tri '()';
h~\ln
nilY
chrqe
ky-
hi~u
h,\ng
I"
-
I 1\)
~
1 ffJ/lx)
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Ta
ell
the
nh,}n
dUQ'C
h;Ull
I neu
tlMY
V1(P(e) hitng
V1,(P(c»)
lrong
bi~u
therc
(2.19).
I(x)
= v P(c)
(2.21 )
TLf
do
ta co the nh,)n
dWJC
hietl
thefC
eua
J(x)
bflllg
d.ch
,ip
dl.lIlg
cong
1111.re:
I~
I .
j(.\)
=
/\
S(c)
(2.22)
eci
;,(,fJ
Oil'
bi2'u
thlre
S(c)
nh(1ll
dUQ'C
tu
pre) h,\ng lhay X
J
Ih~lIlh
x
J
'
x,
th;lllh \
\,;:1 thay
phcp
h(li
(/\)
thanh
phcp
tuyen
(v).
Ta nh(m
IhAy
S(C) sc tuung (rug
J'
-"
vO'i
(]" -1) dinh
ngo~li
trLL'
dinh
tuong
ung voi Pic)
\'~I
duqc gqi
Ii
bicu tlltrc
tuy~n
c~rc
d'.li.
Ctch
bicu
e1ien
hiun
logic
fthong
qua
pIH~P
h,?i
cua
d.c
bi6u
thtTC
tuycn
qrc
d'.li
g<.li
EI
d"ll1g
chui;n
lAc
h()i.
Tiep
Iheo de
co
the
kh,io s:it
l11¢t
d'.lng chu,1n
lftc
nif;.l,
chung
ta
dinh I1ghla
h~lm
lo,~i
trir 16gic
XOR
nhu' sau:
XOR
la phep
101m
bai ng6i
cho
gia
Iri
'J'
nC:u
chi
l11(lt
Hong
hai
IOcln
hang
llh~ln
,~ia
Ir!
'I'
va
nh,:m
gia
Ir!
'()' lrollg
nhiIng tnri:mg
hop
C('H\ lai.
xEBy=
XyA.\.)'
0.23)
Trong
bi~'Ll
Ihtrc trl:n
til
thft)'
n(u
x ho;\c
)'
lu6n nh,)ll gi,i
tq
Ihi blc'u tlILk
:-;0
nhfm
gla
Irj tu'ong
((JIg
theo )'
hO;:lc
theo
x,
co
nghlu
1;1
I
EB.r:::::
x.
Them
vilO
<.16
phep tmln
XOR
EB,
cling
gi6ng
nhu
phep
u)ng.
til(Sa
ll1iln
Illlh ch;'il
giao ho;.tn,
kGt
IH)'p
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phfll1
piloi
va-i
phep
I1h,ln.
DL.ra
\,~IO
cae
tinh
eh,-lt
Iren
la
co
thc dlIa
ra
d',\Ilg
chuftn tftc Iheo
phcp
ta,in
XOR
nlILr
suu.
M()t
hilln 16gic
hfll
k5
1
e6
the
(hrq'c
hicu
dicn
theo
h¢
therc
sau:
./Ix}. '\c'
x, !
:::::.J(x},
x"
X
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}.
(), _I',+},
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x,
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2
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r,.
[.
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.
x)x,
cer
tiep
It,lC
nlur \'(1)' ta sc
nh':.in
dl!'()'C:
/(.1'"
Xc'
x".J
-:::::.
RO
.
()
j.Y
I
Xc
x.,
vI(
I.
().
".
Oi
XIX,
XII
V
v
1(1,1, ,1),,,,,,,
x".
(2.241
Mi1i
s()
IWng
Irong
bi(:u
th(fC
Iren
IiI
m(lt bieu th(rc
IH)i
Cl.rc
IICU
do
d6
chi
co
th0
co
1l1l?1
,tinh
nhfll1
gi,i If'! •
j'
d6i
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tifng
h()
gl[l In
clla
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Thay
ph~p
loan v
btmg
phcp toan
EB
V~l
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mbi x lhay bang
tl\l:'u
tlllJ-c
(It:£;
\',) ta nh(lll
dU\K
hicu
IhlfC
16gic
ILf(ing
(hwng
chi
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27