TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4457 ~ 4
4
6
2
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.548
2
4457
Re
cei
v
ed
De
cem
ber 2
3
, 2013; Re
vi
sed
Febr
uary 17,
2014; Accept
ed March 3, 2
014
A Power Effective Algorithm for State Encoding
Anping He, Hao
Wu, X.
Song
1
, Jinzh
a
o Wu*
2
Guang
xi Ke
y
L
abor
ator
y
of Hybr
id C
o
mputat
ion a
nd IC Des
i
gn An
al
ysis,
Guang
xi Univ
e
r
sit
y
for Natio
n
a
lities, 5
3
0
006,
Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: song2
01
008
26@
163.com
1
,
hidr
w
u
@s
oh
u.com
2
A
b
st
r
a
ct
Red
u
cin
g
the
area a
nd p
o
w
e
r dissi
patio
n
of F
S
M
circuit is of significa
nt imp
o
rtanc
e
for EDA
techno
lo
gy. Many
meth
ods
a
r
e ad
opte
d
to
achi
eve a
n
eff
e
ctive a
nd fast
transformatio
n
of F
S
Ms to bi
nary
codes,
incl
ud
i
ng Ge
netic
al
gorith
m
(GA)
and
oth
e
rs
. In
this
pa
per,
w
e
prop
ose
a
GA b
a
sed
st
ate
assig
n
m
ent of
a F
S
M circuit to gain th
e mini
mi
z
a
t
i
o
n
of pow
er cons
u
m
ption a
nd
area
. W
e
modify t
h
e
traditio
nal
mut
a
tion to b
e
a
n
order
ed o
p
e
ratio
n
, w
h
ich is also a su
bstitution of t
he crossov
e
r that
guar
ante
e
s ev
ery n
e
w
ind
i
vid
ual
ow
ns b
e
tte
r fitness th
an
t
he
old
on
e. W
e
test the
prop
o
s
ed
alg
o
rith
m
w
i
th
benc
h
m
arks,
a
s
w
e
ll
as
do
the c
o
mp
ariso
n
w
i
th the
p
ubl
i
s
hed;
our
met
hod
sav
e
s b
o
t
h
p
o
w
e
r a
n
d
a
r
ea
dissip
a
tio
n
in r
easo
n
a
b
le co
mputatio
n time.
Ke
y
w
ords
:
sta
t
e assign
ment, low
area, low
pow
er, genetic a
l
gorit
hm
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
With the
in
crea
sing
scale
of system
-o
n-ch
ip
(SoC),
the area a
n
d
po
we
r di
ssipation
become
the
critical
con
c
e
r
ns in
VLSI
desi
gn,
e
s
p
e
c
ially fo
r p
o
rt
able
com
puti
ng a
nd
pe
rsonal
comm
uni
cati
on ap
plicatio
ns. Seq
uenti
a
l ci
rcuits, pl
aying a m
a
jo
r rol
e
in VLSI
, is characte
rized
by the output
s de
pen
ding
on both th
e i
nputs
and th
e pa
st state,
e.g., a feedb
ack at the in
p
u
t of
the co
mbinati
onal lo
gic. T
he Finite
stat
e ma
chin
e
(F
SM) is
of a
most
comm
o
n
way of
syst
em
level descri
p
tion for seque
n
t
ial logic.
In EDA tech
n
o
logie
s
, the
automatic sy
nthesi
s
of FS
M to circuit p
l
ays a ve
ry importa
nt
role. Th
e en
coding
pro
c
e
d
u
re of th
e sy
nthesi
s
call
e
d
state a
ssi
gn
ment that ma
ps FSM
state
s
to
binary
codes
is essential for the wh
ole
synthesi
s
, since it will not only affect circuit area but al
s
o
power di
ssip
a
tion with different switchi
ng activi
ties
finally. The
probl
em of finding the st
ate
assignm
ent for minimi
zati
on of power cons
umption a
nd are
a
belo
n
g
s to NP ha
rd
.
The gen
etic a
l
gorithm (GA) is rega
rde
d
as an excelle
nt intelligent sea
r
ch algo
rithm, and
also an effe
ctive method
to achieve fast c
onve
r
g
ence for so
me NP-h
ard
problem
s. Many
investigatio
ns with
GA ha
ve been
do
n
e
for
stat
e a
ssi
gnme
n
ts, su
ch as
[1
-5]
.
Almaini
et al.
demon
strated
that the GA method
pro
duced si
gnifi
cantly simpl
e
r solutio
n
s in
[2]. In
[1],
multi
obje
c
tive GA
ha
s be
en
u
s
ed
to optimi
z
e
both a
r
e
a
and
po
we
r. Ch
attopadh
yay et al. in
[3]
optimize
d
po
wer only, Xia
et al. in [4] o
p
timize
d
both
are
a
an
d po
wer,
Ch
attop
adhyay et al.
[5]
optimize
d
are
a
only. There
are othe
r effe
ctive
method
s ba
sed o
n
symbolic mini
mization [6
-8]
.
Other
heu
ristic algo
rithm
s
h
a
ve be
e
n
propo
se
d: Shiue in
[9] sh
owe
d
a ne
w
comp
re
hen
si
ve method consi
s
ting of
an effici
ent
state minimi
zation a
nd state assi
gnm
ent
techni
que. G
o
ren a
nd Ferguson [10]
prese
n
ted a he
uristi
c for sta
t
e redu
ction of incompl
e
te
ly
specified FS
Ms.
In
th
is
ar
tic
l
e
,
w
e
pr
op
os
e
d
a
n
en
ha
n
c
ed GA
b
a
se
d state
a
ssi
gnme
n
t al
gorithm.
Comp
ari
ng wi
th the original
one, the improveme
n
ts in
clud
e: the number of pop
u
l
ation, removi
ng
the cro
ssove
r ope
ratio
n
a
nd imp
r
oving
the muta
tion
operation.
More
over, wi
th this p
r
opo
se
d
algorith
m
, ea
ch
gene
ratio
n
ha
s o
n
ly o
ne individ
ual,
whi
c
h
ena
bl
es th
e po
pul
ation evolvin
g
via
mutation in
stead of cro
ssover. More i
m
porta
ntly, the enha
nced
mutation op
e
r
ation e
n
sure
s the
new in
dividua
l own
s
better
fitness tha
n
the old on
e. Compa
r
ing
with others, our
algorith
m
sav
e
s
more p
o
wer a
nd are
a
dissi
pation in a re
aso
nabl
e co
mputation tim
e
.
Our pa
pe
r is stru
ctured a
s
follows: in sect
ion 2 we introdu
ce the
state assig
n
m
ent and
the co
st funct
i
on; in se
ctio
n 3,
we sh
ow our GA algo
rithm in
detail and we sh
ow the experime
n
t
and compa
r
i
s
on of our alg
o
r
ithm in se
cti
on 4; we con
c
lud
ed in sect
ion 5.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4457 – 4
462
4458
2.
State Assig
n
ment
and Co
st
Func
tions
In this
paper,
st
at
e
i
s
a ve
ctor,
)
,
,
,
(
2
1
l
s
s
s
S
, of a st
able FSM/
se
quential
-
logi
c output.
The
se
quenti
a
l ci
rcuit i
s
u
s
ually m
odel
ed a
s
Mealy
FSM (with a
s
sumptio
n
of
outputs relating
both input an
d curre
n
t state).
Defini
tion 1.
A
FSM
i
s
a
quintupl
e
0
,
,
,
,
,
S
S
O
I
, where
I
is the
sets of i
nput
s,
O
is
the sets of outputs ,
S
is a set of states,
0
S
is initial
states
,
is the state-tra
n
sitio
n
function:
S
I
S
:
,
is the outp
u
t function:
O
I
S
:
.
EDA tools try
to synthase the FSM to re
al circ
uit
s
; it is a funda
men
t
al proble
m
of how to
encodin
g
the
states
with b
i
nary code
s.
Different
encoding
distin
g
u
ish
e
s th
e switchi
ng a
c
tivates
from on
e bin
a
ry code to
a
nother,
whi
c
h
woul
d finally
affect ci
rcuit are
a
an
d po
wer di
ssip
a
tion.
On the
othe
r
hand, th
e am
ount of
so
rt of
en
codin
g
wo
uld be
hu
ge,
e.g., let
n
be
the total n
u
mb
er
states of
S
, it need
n
s
2
log
(
for up
per b
ound
) st
ate variabl
es
to enco
d
ing t
he state
s
, the
n
according to [11], the total
num
ber of state assi
gnments will be
!
)!
2
(
)!
1
2
(
s
n
s
s
.
For a
concrete state assignm
ent, we
can use
ESPRESSO [12] to generate the
minimized ci
rcuit. The num
ber of the ge
nerate
d
ci
rcui
ts varies
with their en
codi
n
g
method
s, so it
woul
d be
very useful to
fin
d
a
state e
n
coding
co
rr
esp
ondin
g
to le
ss g
a
tes th
at b
e
with l
e
ss
area
and po
we
r co
sumptio
n
co
n
s
eq
uently.
We evaluate
the
state
en
coding
s
by a
c
o
s
t
func
tion.
With the preliminaries in [
1
], the
co
st fun
c
tion
of a tra
n
sitio
n
co
uld b
e
co
mputed by
th
e
produ
ction
of
the
Ham
m
i
ng di
stan
ce
an
d
total transition probability
[13], and th
e
wh
ole
co
st
of a
stat
e g
r
aph
wo
uld
b
e
the
su
m of
all
possibl
e tran
sition
s:
S
s
s
j
i
s
s
j
i
j
i
s
enc
s
enc
HD
tp
C
,
))
(
),
(
(
(1)
3.
A GA
Bas
e
d
Po
w
e
r Effec
t
iv
e Encoding
GA is a heuristic optimi
z
at
ion algo
rithm
imitat
ing the process of n
a
tural evoluti
on, the
solutio
n
of o
p
timization i
s
seen
as in
di
vidual, whi
c
h
expre
s
sed b
y
a variable
seq
uen
ce, ca
lled
chromo
som
e
s. Chromo
so
me is gen
eral
ly expressed
as an alp
hab
etic strin
g
or
nume
r
ic o
ne, and
then to gain the strin
g
is called en
codi
n
g
. While
GA pro
c
e
ssi
ng, it generat
es a
certai
n numb
e
r of
individual
s g
enerally and
rand
omly. In every ge
ne
ration, ea
ch i
ndividual
get
its fitness
b
y
a
spe
c
ific fitness fun
c
tion.
T
he n
e
xt gen
e
r
ation
and
co
mpositio
n
ca
n be
calculat
ed
with
sele
ctin
g
and b
r
ee
ding
operation
s
in term
s of current fi
tness. The mutation exist
s
an
ywhere that
can
gene
rate
ne
w "child" in
di
viduals
alwa
ys by excha
nging th
e p
o
s
ition of t
w
o
gene
s. Fi
gu
re 1
sho
w
s the pseudo
cod
e
for GA.
After long te
rm study of th
e state
and
codi
ng pattern
,
we
find GA based state
e
n
co
ding
algorith
m
wo
uld e
nha
nced
more if
do
some m
odifica
tions, in
clu
d
i
ng the
n
u
mb
er
of po
pulati
on,
removin
g
the
ope
ration
of
cro
s
sove
r, m
odified th
e
way of mutatio
n
an
d the
wa
y cal
c
ulatin
g
the
fitness.
The
main id
ea
of
our algo
rithm
is t
ha
t, every
gen
eratio
n
h
a
s
one
indivi
dual
only, an
d in
each gen
erat
ion, the optimal individua
l is gene
ra
te
d by mutating the one in
d
i
vidual only, then
we
woul
d g
e
t the glo
b
a
l
optimal i
n
d
i
vidual by
compa
r
ing
all
optimal
on
es. Th
e d
e
tailed
explanation i
s
sho
w
n bel
ow.
Initially, we talk a
bout
wh
y every gen
e
r
ation
only h
a
s o
ne in
dividual in thi
s
a
l
gorithm.
There is co
nsidera
b
le amo
unt of populat
ion in tr
aditio
nal GA, and a lot of new individual p
r
o
duct
by cro
s
sover,
in this pro
c
e
ss, the
sea
r
ch regi
o
n
for the assig
n
me
nts is enl
arge
d, meanwhile
, a
sizable
majo
rity individual
of ne
w g
ene
ration d
on’t h
a
ve better fitne
s
s than
the
in
dividual
s of t
h
e
old g
ene
ratio
n
, be
side
s, t
h
is
process
Con
s
um
es
a
lot
of CPU time. So in our algorith
m
every
gene
ration
o
n
ly has one
i
ndividual, the
mutation ta
kes the
pla
c
e
of crossove
r, and
after ev
ery
mutation the new in
dividua
l must have b
e
tter fitnes
s than the old.
Specific m
e
th
od is a
s
follo
ws.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Power Effective Algo
rith
m
for State
Enco
ding (A
npi
ng He
)
4459
Our GA b
a
se
d algo
rithm e
n
co
de
s all FS
M states to a
individual. Let
s
be the amo
unt of
the states,
s
b
2
log
bits bina
ry code for ea
ch
state.
In each ge
neratio
n, we initialize an
individual
ran
domly and t
hen find
a l
o
cal
optimal
assignm
ent. The mutatio
n
is the p
r
im
ary
operation in
this algo
rith
m, which in
cl
ude
s se
ve
ral
swap
s of e
x
chan
ging th
e po
sition of
two
gene
s, after each swap th
e fitness of the individual
would be bette
r or we
kno
ck off the swap. In
detail, the mutation con
s
i
s
ts of two loop
s, the first ge
ne
i
loops fro
m
1 to
n
(
n
is the amount of
gene
s),
while
the se
con
d
gene
j
loop
s from
i
to
n
, if e
x
chan
ging n
o
t
exists, exch
ange thei
r
positio
n an
d
then
cal
c
ul
ate the fitne
ss; if th
e
fitness i
s
bette
r than the
previous, th
en
the
excha
nge
occurs
and
the
n
continue
the loo
p
; if
th
e fitness i
s
not better th
an the
previous,
excha
nge the
two gen
es b
a
ck and th
en
continu
e
the
loops. In the
comp
ari
s
on
pro
c
ed
ure, the
individual
with less produ
ct terms o
w
nin
g
the
better fi
tness, however, if equal, the one
with l
e
ss
swit
chin
g acti
vities woul
d b
e
better. This
method redu
ces a lot of CP
U time.
In each g
ene
ration, we coul
d get a local
optim
al assig
n
ment by so
me step
s of mutation.
At the last mutation, if there is no swap o
c
curs,
we
con
s
ide
r
the cu
rrent individual
is the optimal
assignm
ent; the gen
eratio
n
ends a
nd a n
e
w ge
neratio
n woul
d be ini
t
ialized
contin
ually.
The pseud
o code of pro
p
o
s
ed algo
rithm i
s
as follo
w (Fi
gure 2, Fig
u
re 3 and Figu
re 4)
：
We
explain
the p
s
e
udo
in
detail: In
the
main
fun
c
tio
n
in
Figu
re
2, the lo
op i
n
t
he m
a
in
function
ge
n
e
rate
s th
e lo
cal
optimal
state assi
g
n
m
ent for ea
ch
gene
ration;
the m
a
in fu
nction
outputs the
global
optim
al assig
n
me
nt by co
mp
a
r
ing
all the
state a
s
sign
ments fin
a
lly. The
get_the_l
ocal
_optim
a
function in Figure 3 gene
rate
s the opt
imal assignm
ent for one gen
eration,
the loop there
guara
n
tee th
at exchan
gin
g
any of two gene
s of the i
ndividual not
result in a better
f
i
t
ness,
whi
c
h
call
s
Mutations
fu
nctio
n
in
Figu
re
4. Th
e Mutation
fu
nction
is the
main p
r
o
c
e
d
u
r
e
for the
whol
e
algo
rithm, the Mutation fu
nction
swap t
w
o g
ene
s by
neste
d loo
p
s,
whi
c
h e
n
sures
that any two gene
s can be
swa
ppe
d exc
ept for the on
e has b
een e
x
chan
ged.
Proced
ure pro
pose
d
al
gorith
m
//main function
{
Input (benc
hm
ark file
, numb
e
r
of generati
on)
Loo
p unti
l
gen
eratio
n=
0 //gen
erate al
l the loc
a
l optim
al state
assignm
ent
{
Initializ
e
in
divi
d
ual
(i
ndiv
i
du
al)
Get
the
local
op
tima (individual)
Output
local
optima
Numb
er of gen
eratio
n - 1
}
Output the glo
bal i
ndiv
i
du
al
}
Figure 2. Main Functio
n
Proced
ure GA
{
Create a
n
initi
a
l pop
ulat
i
on of
rand
om ge
nes
Evaluate all c
h
romosom
e
s
Rep
eat
{
Select
chrom
o
somes
w
i
th
the
best fitness to repro
duce
Appl
y
cross
o
ve
r
operator
Appl
y
mutati
on
operator
Eva
l
ua
te
th
e
ne
w
ch
i
l
d
If(child fitness
!
=
any
existing f
i
tness)
Appl
y
termi
nati
on
op
erator
} until termin
a
ti
on con
d
iti
o
n
} end GA
Figure 1. Pro
posed Stru
cture for
Dyna
mic Ov
er
mod
u
lation in DT
C-
CSF Bas
e
d
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KA
Vol. 12, No. 6, June 20
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462
4460
4. Experimenta
l
Result
In this secti
on, we
sh
o
w
the exp
e
ri
ment
al results of the p
r
o
posed alg
o
rit
h
m. We
impleme
n
t ou
r algo
rithm by C++ and Mat
l
ab
with a 2.9
G
Hz AMD CPU and 1.75
GB RAM.
In our
algo
rith
m, each ge
ne
ration
pro
d
u
c
es a l
o
cal opt
imal solution.
Table
1 sho
w
s lo
cal
optimal p
r
o
d
u
c
ed
by eve
r
y
gene
ration
(t
he 2
0
g
ene
ra
tion in th
e fro
n
t), produ
ct t
e
rm
s, switchi
n
g
activity and time com
s
umi
ng, the circui
t designe
rs could ma
ke a
targeted sel
e
ction form so
many local o
p
timal assign
ments.
Table 1. Experime
n
tal Re
sult
generation
1
2
3 4
5 6 7 8 9
10
PT
27
27
23 23
23 24 23 23 23 24
Esw
0.239
0.314
0.267
0.257
0.286
0.311
0.291
0.341
0.285
0.492
Time/sec
3
4
7
9
13 15 17 22 24 26
generation
11
12
13 14
15 16 17 18 19 20
PT
26
25
25 23
26 27 23 23 21 22
Esw
0.334
0.352
0.272
0.329
0.318
0.370
0.288
0.281
0.377
0.326
Time/sec
27
29
31 33
35 37 41 43 45 47
Table 2
sh
o
w
s th
e comp
arison of the
experim
enta
l
results of o
u
r alg
o
rithm
and o
n
e
from M
OGA [
1
] by time
re
quire
ment, lo
w p
o
wer
co
n
s
umptio
n a
n
d
are
a
req
u
ire
m
ent. From t
h
is
table, the are
a
requi
rem
e
n
t
is slightly better
than M
OGA in average, low p
o
wer is
sub
s
tant
ially
equal to the
MOGA, the time for se
eki
n
g the best results is very le
ss tha
n
MOG
A
.
Mutation(
ind
i
vi
dua
l)//main op
erator to find th
e loca
l optima
l
state assignm
e
n
t
{
Loop for (i=0 to i=number
of genes)//first state i
{
Loo
p for (j=
i
to j=
member of g
enes)//seco
nd
state j
{
Exch
an
ge i a
n
d
j gen
e//e
xcha
nge p
o
siti
on of the i and j
Calcu
l
ate
fitne
ss
If fitness better mark the tag of the genes//ha
v
e bee
n e
x
ch
a
nge
d
Else
e
x
ch
an
ge
back
}
}
}
Figure 4. Mutation
Get the local o
p
tima(in
d
iv
idu
a
l
) //generat
e th
e loca
l optima
l
state assignm
e
n
t
{
Loo
p unti
l
ther
e is no e
x
ch
an
ge ha
pp
en in t
h
is lo
op
{
Initial the e
x
c
h
ang
e tag (in
d
ivi
dua
l)
Mutation
(i
ndiv
i
dua
l)
}
}
Figure 3. Get the Local Opt
i
ma
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TELKOM
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ISSN:
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046
A Power Effective Algo
rith
m
for State
Enco
ding (A
npi
ng He
)
4461
Table 2. Experime
n
tal Re
sult
Benchmarks In/out/no.of
state
s
This algorithm
MOGA [
1
]
PT C
Time
PT C
Time
(sec)
bbtas 2/2/6
9
0.502
4sec
9 0.613
1min
10 0.56
11 0.44
bbara
4/2/10
21
0.377
45sec
22 0.49
8min
27 0.39
keyb
7/2/19
44
0.643
7min
46 0.98
3h
47 0.75
55 0.54
Cse 7/7/16
41
0.442
28min
43 0.39
2h
49 0.32
54 0.30
S1 8/6/20
44
1.726
1h4min
43 1.37
6h
53 1.19
60 1.04
S1a 8/6/20
31
1.233
11min
29 1.21
5h19min
30 1.174
Table 3 sho
w
s the
comp
arison of ou
r algorithm
and
th
e
a
l
g
o
r
ithms
in
tr
od
uc
ed
in
[1
4
]
,
[15, 16]. On
averag
e, our algorithm ha
s fewe
r
pro
d
u
ct term
s an
d less
swit
ch
ing activities
in
terms of th
e
results from
[16]. It also o
u
tperfo
rms ot
her metho
d
s
in both
a
r
ea
saving
an
d le
ss
power con
s
u
m
ption.
Table 3. Experime
n
tal Re
sult
Algorith
m
Benchmarks
This algorithm
[14] [15]
[16]
Result Improved
(
%
)
Result Improved
(
%
)
Result
Improved
(
%
)
bbtas
PT
9
-
-
9 0 8
-13
C
0.502
- -
- -
0.815
34
bbara
PT
21
22 5
23 9 24
13
C 0.337
0.317
-6
-
-
0.459
27
key
b
PT
44
46 4
46 4 48
8
C 0.643
0.674
5
-
-
1.469
56
Cse
PT
41
43 5
45 9 46
11
C 0.442
0.355
-26
-
-
0.602
27
S1
PT
44
66 33
68 32 80
45
C 1.726
1.48
-17
-
-
1.698
-2
S1a
PT
31
-
-
66 53 80
61
C
1.233
- -
- - -
-
5. Conclu
sion
In this pa
per,
we p
r
e
s
ente
d
a FSM
state
en
codi
ng p
r
ocedu
re fo
r
redu
cin
g
the
power
and a
r
ea
co
nsum
ption of
circuits. Ou
r algorit
hm b
a
se
s on GA,
the enhan
cements i
n
clu
de:
removem
ent
of the o
peration of
crosso
ver an
d m
o
d
i
fied the
ope
ration
of mut
a
tion. With
the
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4457 – 4
462
4462
comp
ari
s
o
n
o
f
the publish
e
d
algorith
m
s,
ours sh
ow
s i
t
s st
ro
ng ef
f
e
ct
s.
I
n
sh
ort
,
we r
ega
rd ou
r
algorith
m
more suitabl
e for area/p
o
wer o
p
timized
reali
z
ation of FS
Ms.
Our future work i
s
focu
se
d on two direction
s
: firstl
y, we improv
e the efficien
cy of the
mutation ope
ration sin
c
e th
e most swap
s in mutation may be unne
ce
ssary; se
co
ndly, we sho
u
l
d
improve the
model of po
wer co
nsumma
tion more a
ccurate.
Ackn
o
w
l
e
dg
ements
This
wo
rk is partly supp
orted
by Bagui
sch
o
larship p
r
oje
c
t, the Natu
ral
Scien
c
e
Found
ation o
f
Guangxi un
der G
r
ant No
. 2011GXNS
F
A0181
54 an
d 2012GX
N
S
F
GA060
003,
the
Scien
c
e a
n
d
Tech
nolo
g
y Found
ation
of Guangxi
unde
r Gran
t No. 1016
9
-
1, and G
u
a
ngxi
Scientific Re
search
Project
No.201
012M
S274 , Funde
d Proje
c
ts of
Innovation Pl
an for Gu
ang
xi
Grad
uate Ed
ucatio
n No.g
xun-chx201
3t18 an
d G
uan
gx
i Univers
i
ty
for
Nationalities
P
r
ojec
t, No.
2012
QD017
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