– 18 – 2017-01-24 – main –
Softw
are
Desig
n,
Modellin
gand
Analysis
inU
ML
Lectu
re18:
Live
Seq
uen
ceC
harts
II
2017-0
1-2
4
Pro
f.Dr.A
nd
reas
Po
de
lski,Dr.B
ern
dW
estp
hal
Alb
ert-Lu
dw
igs-Un
iversität
Freib
urg,G
erm
any
Co
nten
t
– 18 – 2017-01-24 – Scontent –
2/
66
•R
efle
ctiveD
escrip
tion
so
fB
eh
aviou
r
•In
teractio
ns
•A
Brie
fH
istory
of
Se
qu
en
ceD
iagrams
•L
iveS
eq
ue
nce
Ch
arts
•A
bstract
Sy
ntax,W
ell-Fo
rme
dn
ess
•S
em
antics
•T
BA
Co
nstru
ction
for
LSC
Bo
dy
•C
uts,F
ired
sets
•S
ignal/
Attrib
ute
Exp
ressio
ns
•Lo
op
/P
rogre
ssC
on
ditio
ns
•E
xcursio
n:B
üch
iAu
tom
ata
•Lan
gu
ageo
fa
Mo
de
l
•Fu
llLSC
s
•E
xisten
tialand
Un
iversal
•P
re-C
harts
•Fo
rbid
de
nS
cen
arios
•LS
Cs
and
Tests
Th
eP
lan
– 18 – 2017-01-24 – Splan –
3/
66
6.B
7.A7.B
•T
hu
,19
.1.:L
iveS
eq
ue
nce
Ch
artsI
•F
irstly:S
tate-M
achin
es
Re
st,Co
de
Ge
ne
ration
•Tu
e,
24
.1.:L
iveS
eq
ue
nce
Ch
artsII
•T
hu
,2
6.
1.:Live
Se
qu
en
ceC
harts
III•
•
•Tu
e,
31.
1.:Tuto
rial7•
•T
hu
,2
.2.:M
od
elB
ased
/D
riven
SW
En
gin
ee
ring
•
•M
on
,6
.2.:In
he
ritance
•Tu
e,
7.2.:M
eta-M
od
ellin
g+
Qu
estio
ns
Feb
ruary,17th
:Th
eE
xam.
Co
nstru
ctiveB
eha
viou
ral
Mo
dellin
gin
UM
L:
Discu
ssion
– 18 – 2017-01-24 – main –
4/
66
Sem
an
ticVa
riatio
nP
oin
ts
– 18 – 2017-01-24 – Ssemvar –
5/
66
Pe
ssimistic
view
:Th
ere
areto
om
any...
•Fo
rin
stance
,
•allo
wab
sen
ceo
fin
itialpse
ud
o-state
so
bje
ctm
ayth
en
“be”
ine
nclo
sing
statew
itho
ut
be
ing
inan
ysu
bstate
;o
rassu
me
on
eo
fth
ech
ildre
nstate
sn
on
-de
term
inistically
•(im
plicitly)e
nfo
rced
ete
rmin
ism,e
.g.b
yco
nsid
erin
gth
eo
rde
rin
wh
ichth
ings
have
be
en
add
ed
toth
eC
AS
Eto
ol’s
rep
osito
ry,o
rso
me
graph
icalord
er
(left
torigh
t,top
tob
otto
m)
•allo
wtru
eco
ncu
rren
cy
•e
tc.etc.
Exe
rcise:S
earch
the
stand
ardfo
r“se
man
ticalvariation
po
int”.
•C
rane
and
Din
gel(2
00
7),e.g.,p
rovid
ean
in-d
ep
thco
mp
arison
of
State
mate
,UM
L,an
dR
hap
sod
ystate
mach
ine
s—
the
bo
ttom
line
is:
•th
ein
terse
ction
isn
ot
em
pty
(i.e.so
me
diagram
sm
ean
the
same
toallth
ree
com
mu
nitie
s)
•n
on
eis
the
sub
set
of
ano
the
r(i.e
.each
pair
of
com
mu
nitie
sh
asd
iagrams
me
anin
gd
iffere
nt
thin
gs)
Op
timistic
view
:
•to
ols
exist
with
com
ple
tean
dco
nsiste
nt
cod
ege
ne
ration
.
•go
od
mo
de
lling-gu
ide
line
scan
con
tribu
teto
avoid
ing
misu
nd
erstan
din
gs.
Refl
ectiveD
escriptio
ns
of
Beh
avio
ur
– 18 – 2017-01-24 – main –
6/
66
Co
nstru
ctivevs.
Refl
ectiveD
escriptio
ns
– 18 – 2017-01-24 – Sreflective –
7/
66
Hare
l(199
7)p
rop
ose
sto
distin
guish
con
structive
and
refle
ctived
escrip
tion
s:
•A
con
structive
de
scriptio
nte
llsu
sh
ow
thin
gsare
com
pu
ted
:
“Ala
ngua
geis
co
nstru
ctiv
eif
itco
ntrib
utesto
the
dyn
am
icsem
an
ticso
fth
em
od
el.
Th
at
is,itsco
nstructs
con
tain
info
rma
tion
need
edin
executing
the
mo
del
or
intra
nsla
ting
itin
toexecuta
ble
cod
e.”
•A
refle
ctived
escrip
tion
tells
us
wh
atsh
all(or
shalln
ot)b
eco
mp
ute
d:
“Oth
erla
ngua
gesa
rere
flectiv
eo
ra
sse
rtive,
an
dca
nb
eused
by
the
systemm
od
elerto
cap
turep
arts
of
the
thin
king
tha
tgo
into
build
ing
the
mo
del–
beh
avio
rin
cluded
–,
tod
erivea
nd
presen
tview
so
fth
em
od
el,statica
llyo
rd
uring
execution
,
or
toset
con
strain
tso
nb
eha
vior
inp
repa
ratio
nfo
rverifica
tion
.”
No
te:N
osh
arpb
ou
nd
aries!(W
ou
ldb
eto
oe
asy.)
Intera
ction
sa
sR
eflective
Descrip
tion
– 18 – 2017-01-24 – Sinteract –
8/
66
•In
UM
L,re
flective
(tem
po
ral)de
scriptio
ns
aresu
bsu
me
db
yin
teractio
ns.
AU
ML
mo
de
lM=
(C
D,S
M,O
D,I
)h
asa
set
of
inte
raction
sI
.
•A
nin
teractio
nI∈
Ican
be
(OM
Gclaim
:eq
uivale
ntly)d
iagram
me
das
•co
mm
un
ication
diag
ram(fo
rme
rlykn
ow
nas
collab
oratio
nd
iagram),
•tim
ing
diag
ram,o
r
•se
qu
en
ced
iagram
.
Fig
ure
14
.27
- Co
mm
un
icatio
n d
iag
ram
sd
M
:rs[k
]:B
s[u
]:B
1a:m
1
2:m
21b:m
3
1b.1
:m3
1b.1
.1:m
3,
1b.1
.1.1
:m2
Life
line
Me
ssa
ge
with
Seq
uen
ce
nu
mbe
r
Me
ssa
ge
s
(OM
G,2
00
7,5
15)
Fig
ure
14
.30 - C
om
pa
ct L
ifelin
e w
ith S
tate
s
sd
Use
rAcc_
Use
r
Idle
WaitC
ard
WaitA
cce
ss
Idle
{d..3
*d}
:User
Sta
te o
r co
nd
ition
Life
line
Dura
tion
Constra
int
(OM
G,2
00
7,5
22
)
Fig
ure
14
.31 - T
imin
g D
iag
ram
with
mo
re th
an
on
e L
ifelin
e a
nd
with
Mes
sag
es
sd
Use
rAcce
pte
d
Idle
WaitC
ard
WaitA
ccess
{t..t+3}
{d..3
*d}
:User
01
2t
HasC
ard
NoC
ard
:ACSystem
Code
Card
Out
{0..1
3}
OK
Unlo
ck
dt=
now
Sta
te o
r con
ditio
nL
ifelin
es
Du
ratio
n O
bse
rva
tion
Du
ratio
n C
onstra
ints
Tim
e O
bserv
atio
n
Tim
e C
on
stra
int
Me
ssa
ge
(OM
G,2
00
7,5
22
)
Fig
ure
14
.26
- Seq
uen
ce
Dia
gra
m w
ith tim
e a
nd
timin
g c
on
cep
ts
sd
Use
rAcce
pte
d
:User
:AC
Syste
m
Code d
=d
ura
tion
Ca
rdO
ut {0
..13}
OK
Un
lock
{d..3
*d}
t=n
ow
{t..t+3
}
Du
ratio
nC
on
stra
int
Tim
eO
bse
rva
tion
Tim
eC
on
stra
int
Du
ratio
nO
bse
rva
tion
(OM
G,2
00
7,5
13)
Intera
ction
sa
sR
eflective
Descrip
tion
– 18 – 2017-01-24 – Sinteract –
8/
66
•In
UM
L,re
flective
(tem
po
ral)de
scriptio
ns
aresu
bsu
me
db
yin
teractio
ns.
AU
ML
mo
de
lM=
(C
D,S
M,O
D,I
)h
asa
set
of
inte
raction
sI
.
•A
nin
teractio
nI∈
Ican
be
(OM
Gclaim
:eq
uivale
ntly)d
iagram
me
das
•co
mm
un
ication
diag
ram(fo
rme
rlykn
ow
nas
collab
oratio
nd
iagram),
•tim
ing
diag
ram,o
r
•se
qu
en
ced
iagram
.
Fig
ure
14
.27
- Co
mm
un
icatio
n d
iag
ram
sd
M
:rs[k
]:B
s[u
]:B
1a:m
1
2:m
21b:m
3
1b.1
:m3
1b.1
.1:m
3,
1b.1
.1.1
:m2
Life
line
Me
ssa
ge
with
Seq
uen
ce
nu
mbe
r
Me
ssa
ge
s
(OM
G,2
00
7,5
15)
Fig
ure
14
.30 - C
om
pa
ct L
ifelin
e w
ith S
tate
s
sd
Use
rAcc_
Use
r
Idle
WaitC
ard
WaitA
cce
ss
Idle
{d..3
*d}
:User
Sta
te o
r co
nd
ition
Life
line
Dura
tion
Constra
int
(OM
G,2
00
7,5
22
)
Fig
ure
14
.31 - T
imin
g D
iag
ram
with
mo
re th
an
on
e L
ifelin
e a
nd
with
Mes
sag
es
sd
Use
rAcce
pte
d
Idle
WaitC
ard
WaitA
ccess
{t..t+3}
{d..3
*d}
:User
01
2t
HasC
ard
NoC
ard
:ACSystem
Code
Card
Out
{0..1
3}
OK
Unlo
ck
dt=
now
Sta
te o
r con
ditio
nL
ifelin
es
Du
ratio
n O
bse
rva
tion
Du
ratio
n C
onstra
ints
Tim
e O
bserv
atio
n
Tim
e C
on
stra
int
Me
ssa
ge
(OM
G,2
00
7,5
22
)
Fig
ure
14
.26
- Seq
uen
ce
Dia
gra
m w
ith tim
e a
nd
timin
g c
on
cep
ts
sd
Use
rAcce
pte
d
:User
:AC
Syste
m
Code d
=d
ura
tion
Ca
rdO
ut {0
..13}
OK
Un
lock
{d..3
*d}
t=n
ow
{t..t+3
}
Du
ratio
nC
on
stra
int
Tim
eO
bse
rva
tion
Tim
eC
on
stra
int
Du
ratio
nO
bse
rva
tion
(OM
G,2
00
7,5
13)
Fig
ure
14
.28 - In
tera
ctio
n O
ve
rvie
w D
iag
ram
rep
rese
ntin
g a
Hig
h L
evel In
tera
ctio
n d
iag
ram
sd
Ove
rvie
wD
iagra
m life
line
s :U
ser, :A
CS
yste
m
ref
Esta
blis
hA
ccess("Ille
ga
l PIN
")
sd
:User
:AC
Syste
m
Card
Outs
d
:User
:AC
Syste
m
Msg("P
lease E
nte
r")
ref
Op
en
Do
or
[pin
ok]
{0..2
5}
{1..1
4}
Inte
ractio
nU
se
(inlin
e) In
tera
ctio
n
de
cis
ion
inte
ractio
n c
on
stra
int
Dura
tion
Con
stra
int
(OM
G,2
00
7,5
18)
Wh
yS
equ
ence
Dia
gra
ms?
– 18 – 2017-01-24 – Sinteract –
9/
66
Mo
stP
rom
ine
nt:S
eq
ue
nce
Diagram
s—
with
lon
gh
istory
:
•M
essage
Se
qu
en
ceC
harts,stan
dard
ized
by
the
ITU
ind
iffere
nt
versio
ns,
ofte
naccu
sed
tolack
afo
rmalse
man
tics.
•S
eq
ue
nce
Diag
rams
of
UM
L1.x
Mo
stse
vere
draw
backs
of
the
sefo
rmalism
s:
•u
ncle
arin
terp
retatio
n:
exam
ple
scen
arioo
rin
variant?
•u
ncle
aractivatio
n:
wh
attrigge
rsth
ere
qu
irem
en
t?
•u
ncle
arp
rog
ress
req
uire
me
nt:
mu
stallm
essage
sb
eo
bse
rved
?
•co
nd
ition
sm
ere
lyco
mm
en
ts
•n
om
ean
sto
exp
ress
forb
idd
en
scen
arios
Use
rC
oin
Valid
ator
Ch
oice
Pan
el
Disp
en
ser
C50
pWATER
water
_in
_sto
ck
dWATER
OK
Hen
ce:L
iveS
equ
ence
Ch
arts
– 18 – 2017-01-24 – Sinteract –
10/
66
•S
Ds
of
UM
L2
.xad
dre
ssso
me
issue
s,ye
tth
estan
dard
exh
ibits
un
clarities
and
eve
nco
ntrad
iction
sH
arelan
dM
aoz
(20
07
);Stö
rrle(2
00
3)
•Fo
rth
ele
cture
,we
con
side
rL
iveS
eq
ue
nce
Ch
arts(L
SC
s)Dam
man
dH
arel(2
00
1);Klo
se(2
00
3);H
arelan
dM
arelly
(20
03
),w
ho
have
aco
mm
on
fragme
nt
with
UM
L2
.xS
Ds
Hare
land
Mao
z(2
00
7)
•M
od
ellin
gg
uid
elin
e:stick
toth
atfragm
en
t.
LS
C:
bu
yw
ater
AC
:true
AM
:in
variant
I:strict
Use
rC
oin
Valid
ator
cp:C
ho
iceP
ane
lD
ispe
nse
r
C50
pWATER
¬(C
50!∨E1!∨pSOFT!
∨pTEA!∨pFIL
LUP!
cp->water
_in
_sto
ck
dWATER
OK
¬(dSoft!
∨dTEA!)
Co
urse
Ma
p
– 18 – 2017-01-24 – main –
11/6
6
UM
L
ModelInstances
NS
WE
CD
,SM
S=
(T,C,V
,atr),S
M
M=
(ΣDS,A
S,→
SM)
ϕ∈
OC
L
expr
CD
,SD
S,S
D
B=
(QSD,q
0 ,AS,→
SD,F
SD)
π=
(σ0 ,ε
0 )(cons0,Snd0)
−−−−−−−−→
u0
(σ1 ,ε
1 )···
wπ=
((σi ,co
nsi ,S
ndi ))
i∈N
G=
(N,E
,f)
Ma
them
atics
OD
UM
L
✔✔
✔✔
✔✔
✔
✔
✔
✔
Live
Seq
uen
ceC
ha
rts—
Syn
tax
– 18 – 2017-01-24 – main –
12/
66
LS
CB
od
yB
uild
ing
Blo
cks
– 18 – 2017-01-24 – Slscsyn –
13/
66
:C
1:C
2
x>
3
:C
3
ABC
D
E
v=
0
LS
CB
od
y:A
bstra
ctS
ynta
x
– 18 – 2017-01-24 – Slscsyn –
15/
66
De
finitio
n.[LS
CB
od
y]
An
LS
Cb
od
yo
ver
signatu
reS
=(T,C,V,atr,E)
isa
tup
le
((L,�,∼
),I,Msg,Cond,LocInv,Θ
)
wh
ere
•L
isa
finite
,no
n-e
mp
tyo
flo
cation
sw
ith
•a
partialo
rde
r�
⊆L
×L
,
•a
sym
me
tricsim
ultan
eity
relatio
n∼
⊆L
×L
disjo
int
with
�,i.e
.�∩
∼=
∅,
•I
={I1,...,In}
isa
partitio
nin
go
fL
;ele
me
nts
ofI
arecalle
din
stance
line
,
•Msg
⊆L
×E
×L
isa
set
of
me
ssages
with
(l,E,l′)
∈Msg
on
lyif(l,l′)
∈≺
∪∼
;
me
ssage(l,E,l′)
iscalle
din
stantan
eo
us
iffl∼l′
and
asyn
chro
no
us
oth
erw
ise,
•Cond⊆
(2L
\∅)×
Expr
Sis
ase
to
fco
nd
ition
sw
ith(L,φ)∈
Cond
on
lyifl∼l′
for
alll6=l′∈L
,
•LocInv⊆L
×{◦,•}×
Expr
S×L
×{◦,•}
isa
set
of
localin
variants
with
(l,ι,φ,l′,ι′)
∈LocInv
on
lyifl≺l′,◦
:exclu
sive,•
:inclu
sive,
•Θ
:L
∪Msg
∪Cond∪
LocInv→
{hot,cold}
assigns
toe
achlo
cation
and
each
ele
me
nt
ate
mp
eratu
re.
Fro
mC
on
creteto
Ab
stract
Syn
tax
– 18 – 2017-01-24 – Slscsyn –
16/
66
•lo
cation
sL
,
•�
⊆L
×L
,∼
⊆L
×L
•I
={I1,...,In}
,
•Msg
⊆L
×E×L
,
•Cond⊆
(2L
\∅)×
Expr
S
•LocInv⊆L
×{◦,•}×
Expr
S×L
×{◦,•}
,
•Θ
:L
∪Msg
∪Cond∪
LocInv→
{hot,cold}
.
:C
1:C
2
x>
3
:C
3
ABC
D
E
v=
0
Fro
mC
on
creteto
Ab
stract
Syn
tax
– 18 – 2017-01-24 – Slscsyn –
16/
66
•lo
cation
sL
,
•�
⊆L
×L
,∼
⊆L
×L
•I
={I1,...,In}
,
•Msg
⊆L
×E×L
,
•Cond⊆
(2L
\∅)×
Expr
S
•LocInv⊆L
×{◦,•}×
Expr
S×L
×{◦,•}
,
•Θ
:L
∪Msg
∪Cond∪
LocInv→
{hot,cold}
.
:C
1:C
2
x>
3
:C
3
ABC
D
E
v=
0
l1,0
l1,1
l1,2
l1,3
l1,4
l2,0
l2,1
l2,2
l2,3
l3,0
l3,1
l3,2
Fro
mC
on
creteto
Ab
stract
Syn
tax
– 18 – 2017-01-24 – Slscsyn –
16/
66
•lo
cation
sL
,
•�
⊆L
×L
,∼
⊆L
×L
•I
={I1,...,In}
,
•Msg
⊆L
×E×L
,
•Cond⊆
(2L
\∅)×
Expr
S
•LocInv⊆L
×{◦,•}×
Expr
S×L
×{◦,•}
,
•Θ
:L
∪Msg
∪Cond∪
LocInv→
{hot,cold}
.
Well-F
orm
edn
ess
– 18 – 2017-01-24 – Slscsyn –
17/
66
Bo
nd
ed
ne
ss/n
oflo
ating
con
ditio
ns:(co
uld
be
relaxe
da
littleif
we
wan
ted
to)
•Fo
re
achlo
cationl∈L
,ifl
isth
elo
cation
of
•a
con
ditio
n,i.e
.∃(L,φ
)∈Cond:l∈L
,or
•a
localin
variant,i.e
.∃(l1,ι
1,φ,l2,ι
2 )∈LocIn
v:l∈{l1,l2 }
,
the
nth
ere
isa
locatio
nl ′
simu
ltane
ou
stol,i.e
.l∼l ′,w
hich
isth
elo
cation
of
•an
instan
ceh
ead
,i.e.l ′
ism
inim
alwrt.�
,or
•a
me
ssage,i.e
.
∃(l1,E,l2 )
∈Msg
:l∈{l1,l2 }
.
No
te:
ifm
essage
sin
ach
artare
cyclic,
the
nth
ere
do
esn’t
exist
ap
artialord
er
(sosu
chd
iagrams
do
n’t
eve
nh
avean
abstract
syn
tax).
Live
Seq
uen
ceC
ha
rts—
Sem
an
tics
– 18 – 2017-01-24 – main –
18/
66
TB
A-b
ased
Sem
an
ticso
fL
SC
s
– 18 – 2017-01-24 – Slscpresem –
19/
66
UM
L
ModelInstances
NS
WE
CD
,SM
S=
(T,C,V
,atr),S
M
M=
(ΣDS,A
S,→
SM)
ϕ∈
OC
L
expr
CD
,SD
S,S
D
B=
(QSD,q
0 ,AS,→
SD,F
SD)
π=
(σ0 ,ε
0 )(cons0,Snd0)
−−−−−−−−→
u0
(σ1 ,ε
1 )···
wπ=
((σi ,co
nsi ,S
ndi ))
i∈N
G=
(N,E
,f)
Ma
them
atics
OD
UM
L
✔✔
✔✔
✔
✘
✔
✘
✘✔
✔
✔
✔
✔
Plan
:
(i)G
iven
anL
SC
Lw
ithb
od
y((L,�,∼
),I,M
sg,C
ond,L
ocIn
v,Θ
),
(ii)co
nstru
cta
TB
AB
L,an
d
(iii)d
efin
elan
guage
L(L
)o
fL
inte
rms
ofL(B
L),
inp
articular
taking
activation
con
ditio
nan
dactivatio
nm
od
ein
toacco
un
t.
(iv)d
efin
elan
guage
L(M
)o
fa
UM
Lm
od
el.
•T
he
nM
|=L
(un
iversal)
ifan
do
nly
ifL(M
)⊆
L(L
).
An
dM
|=L
(existe
ntial)
ifan
do
nly
ifL(M
)∩L(L
)6=
∅.
Live
Seq
uen
ceC
ha
rts—
TB
AC
on
structio
n
– 18 – 2017-01-24 – main –
20
/6
6
Fo
rma
lL
SC
Sem
an
tics:It’s
inth
eC
uts!
– 18 – 2017-01-24 – Slsccutfire –
21/
66
De
finitio
n.
Let((L
,�,∼
),I,M
sg,C
ond,L
ocIn
v,Θ
)b
ean
LS
Cb
od
y.
An
on
-em
pty
set∅6=C
⊆L
iscalle
da
cut
of
the
LS
Cb
od
yiff
•it
isd
ow
nw
ardclo
sed
,i.e.∀l,l ′•l ′∈C
∧l�l ′
=⇒
l∈C,
•it
isclo
sed
un
de
rsim
ultan
eity
,i.e.
∀l,l ′
•l ′∈C
∧l∼l ′
=⇒
l∈C
,and
•it
com
prise
sat
least
on
elo
cation
pe
rin
stance
line
,i.e.
∀i∈I∃l∈C
•il=i.
Fo
rma
lL
SC
Sem
an
tics:It’s
inth
eC
uts!
– 18 – 2017-01-24 – Slsccutfire –
21/
66
De
finitio
n.
Let((L
,�,∼
),I,M
sg,C
ond,L
ocIn
v,Θ
)b
ean
LS
Cb
od
y.
An
on
-em
pty
set∅6=C
⊆L
iscalle
da
cut
of
the
LS
Cb
od
yiff
•it
isd
ow
nw
ardclo
sed
,i.e.∀l,l ′•l ′∈C
∧l�l ′
=⇒
l∈C,
•it
isclo
sed
un
de
rsim
ultan
eity
,i.e.
∀l,l ′
•l ′∈C
∧l∼l ′
=⇒
l∈C
,and
•it
com
prise
sat
least
on
elo
cation
pe
rin
stance
line
,i.e.
∀i∈I∃l∈C
•il=i.
Th
ete
mp
eratu
refu
nctio
nis
exte
nd
ed
tocu
tsas
follo
ws:
Θ(C
)=
{
hot
,if∃l∈C
•(∄l ′∈C
•l≺l ′)
∧Θ(l)
=hot
cold
,oth
erw
ise
that
is,Cis
ho
tif
and
on
lyif
atle
asto
ne
of
itsm
aximale
lem
en
tsis
ho
t.
Cu
tE
xam
ples
– 18 – 2017-01-24 – Slsccutfire –
22
/6
6
∅6=C
⊆L
—d
ow
nw
ardclo
sed
—sim
ultan
eity
close
d—
atle
asto
ne
loc.p
er
instan
celin
e
:C
1:C
2
φ
:C
3
E
F
G
l1,0
l1,1
l1,2
l2,0
l2,1
l2,2
l2,3
l3,0
l3,1
AS
uccesso
rR
elatio
no
nC
uts
– 18 – 2017-01-24 – Slsccutfire –
23
/6
6
Th
ep
artialord
er
“�”
and
the
simu
ltane
ityre
lation
“∼”
of
locatio
ns
ind
uce
ad
irect
succe
ssor
relatio
no
ncu
tso
fan
LS
Cb
od
yas
follo
ws:
De
finitio
n.
LetC
⊆L
be
ta
cut
of
LS
Cb
od
y((L
,�,∼
),I,Msg,Cond,LocIn
v,Θ
).
Ase
t∅6=F
⊆L
of
locatio
ns
iscalle
dfire
d-se
tF
of
cutC
ifan
do
nly
if
•C
∩F
=∅
andC
∪F
isa
cut,i.e
.Fis
close
du
nd
er
simu
ltane
ity,
•alllo
cation
sinF
ared
irect
≺-su
ccesso
rso
fth
efro
nt
ofC
,i.e.
∀l∈F
∃l ′∈C
•l ′≺l∧(∄l ′′
∈C
•l ′≺l ′′
≺l),
•lo
cation
sinF
,that
lieo
nth
esam
ein
stance
line
,arep
airwise
un
ord
ere
d,i.e
.
∀l6=l ′∈F
•(∃I∈
I•{l,l ′}
⊆I)
=⇒
l6�l ′∧l ′6�l,
•fo
re
achasy
nch
ron
ou
s(!)
me
ssagere
cep
tion
inF
,th
eco
rresp
on
din
gse
nd
ing
isalre
ady
inC
,
∀(l,E
,l ′)∈
Msg
•l ′∈F
=⇒
l∈C.
Th
ecu
tC
′=C
∪F
iscalle
dd
irect
succe
ssor
ofC
viaF
,de
no
ted
byC FC
′.
Sig
na
la
nd
Attrib
ute
Exp
ression
s
– 18 – 2017-01-24 – Stbaconstr –
26
/6
6
•Le
tS
=(T,C,V,atr,E)
be
asign
ature
andX
ase
to
flo
gicalvariable
s,
•T
he
signalan
dattrib
ute
exp
ressio
nsExpr
S(E,X)
ared
efin
ed
by
the
gramm
ar:
ψ::=
true|ψ|E
!x,y
|E
?x,y
|¬ψ|ψ
1∨ψ
2,
wh
ere
expr:Bool∈Expr
S,E
∈E
,x,y
∈X
(or
key
wo
rdenv
).
•W
eu
seE!? (X
):=
{E
!x,y,E
?x,y
|E
∈E,x,y
∈X}
tod
en
ote
the
set
of
eve
nt
exp
ressio
ns
ove
rE
andX
.
TB
AC
on
structio
nP
rincip
le
– 18 – 2017-01-24 – Stbaconstr –
27
/6
6
Re
call:Th
eT
BAB(L
)o
fL
SC
Lis(E
xprB(X
),X,Q,q
ini ,→
,QF)
with
•Q
isth
ese
to
fcu
tso
fL
,qin
iis
the
instan
ceh
ead
scu
t,
•ExprB
=Φ
∪E!?(X
),
•→
con
sistso
flo
op
s,pro
gress
transitio
ns
(from F
),and
legale
xits(co
ldco
nd
./lo
calinv.),
•F
={C
∈Q
|Θ(C
)=
cold
∨C
=L}
isth
ese
to
fco
ldcu
ts.
TB
AC
on
structio
nP
rincip
le
– 18 – 2017-01-24 – Stbaconstr –
27
/6
6
Re
call:Th
eT
BAB(L
)o
fL
SC
Lis(E
xprB(X
),X,Q,q
ini ,→
,QF)
with
•Q
isth
ese
to
fcu
tso
fL
,qin
iis
the
instan
ceh
ead
scu
t,
•ExprB
=Φ
∪E!?(X
),
•→
con
sistso
flo
op
s,pro
gress
transitio
ns
(from F
),and
legale
xits(co
ldco
nd
./lo
calinv.),
•F
={C
∈Q
|Θ(C
)=
cold
∨C
=L}
isth
ese
to
fco
ldcu
ts.
So
inth
efo
llow
ing,w
e“o
nly”
ne
ed
toco
nstru
ctth
etran
sition
s’labe
ls:
→=
{(q,
,q)|q∈Q}∪
{(q,
,q′)
|q Fq′}
∪{(q,
,L)|q∈Q}
TB
AC
on
structio
nP
rincip
le
– 18 – 2017-01-24 – Stbaconstr –
27
/6
6
Re
call:Th
eT
BAB(L
)o
fL
SC
Lis(E
xprB(X
),X,Q,q
ini ,→
,QF)
with
•Q
isth
ese
to
fcu
tso
fL
,qin
iis
the
instan
ceh
ead
scu
t,
•ExprB
=Φ
∪E!?(X
),
•→
con
sistso
flo
op
s,pro
gress
transitio
ns
(from F
),and
legale
xits(co
ldco
nd
./lo
calinv.),
•F
={C
∈Q
|Θ(C
)=
cold
∨C
=L}
isth
ese
to
fco
ldcu
ts.
So
inth
efo
llow
ing,w
e“o
nly”
ne
ed
toco
nstru
ctth
etran
sition
s’labe
ls:
→=
{(q,ψ
loop(q
),q)|q∈Q}∪
{(q,ψ
prog(q,q′),q′)
|q Fq′}
∪{(q,ψ
exit (q
),L)|q∈Q}
TB
AC
on
structio
nP
rincip
le
– 18 – 2017-01-24 – Stbaconstr –
27
/6
6
Re
call:Th
eT
BAB(L
)o
fL
SC
Lis(E
xprB(X
),X,Q,q
ini ,→
,QF)
with
•Q
isth
ese
to
fcu
tso
fL
,qin
iis
the
instan
ceh
ead
scu
t,
•ExprB
=Φ
∪E!?(X
),
•→
con
sistso
flo
op
s,pro
gress
transitio
ns
(from F
),and
legale
xits(co
ldco
nd
./lo
calinv.),
•F
={C
∈Q
|Θ(C
)=
cold
∨C
=L}
isth
ese
to
fco
ldcu
ts.
So
inth
efo
llow
ing,w
e“o
nly”
ne
ed
toco
nstru
ctth
etran
sition
s’labe
ls:
→=
{(q,ψ
loop(q
),q)|q∈Q}∪
{(q,ψ
prog(q,q′),q′)
|q Fq′}
∪{(q,ψ
exit (q
),L)|q∈Q}
q...
ψloop(q
):“w
hat
allo
ws
us
tosta
yat
cutq”
“...F
1”
ψprog(q,q′):
“chara
cte
ris
atio
nof
fire
dsetFn”
ψexit (q
):“w
hatallo
ws
us
to
legally
exit”
true
:C
1:C
2
x>
3
:C
3
ABC
DE
v=
0
TB
AC
on
structio
nP
rincip
le
– 18 – 2017-01-24 – Stbaconstr –
28
/6
6
“On
ly”co
nstru
ctth
etran
sition
s’labe
ls:
→=
{(q,ψ
loop(q
),q)|q∈Q}∪
{(q,ψ
prog(q,q′),q′)
|q Fq′}
∪{(q,ψ
exit (q
),L)|q∈Q}
q
q1
...qn
ψloop(q
)=
=:ψ
hot
loop(q)
︷︸︸
︷
ψMsg(q
)∧ψ
LocInv
hot
(q)∧ψ
LocInv
cold
(q)
ψexit (q
)=
(ψ
hot
loop(q
)∧
¬ψ
LocInv
cold
(q))
∨∨
1≤i≤n
(ψ
hot
prog(q,qi )
∧(¬ψ
LocInv,•
cold
(q,qi )∨¬ψ
Cond
cold
(q,qi )))
ψprog(q,qn)=
=:ψ
hot
prog(q,qn)
︷︸︸
︷
ψMsg(q
,qn)∧ψ
Cond
hot(q,qn)∧ψ
LocInv,•
hot
(q,qn)
∧ψ
Cond
cold
(q,qn)∧ψ
LocInv,•
cold
(q,qn)
true:C
1:C
2
x>
3
:C
3
ABC
DE
v=
0
Lo
op
Co
nd
ition
– 18 – 2017-01-24 – Stbaconstr –
29
/6
6
ψloop(q
)=ψ
Msg(q
)∧ψ
LocInv
hot
(q)∧ψ
LocInv
cold
(q)
•ψMsg(q
)=
¬∨
1≤i≤nψMsg(q
,qi )
∧(stric
t=⇒
∧
ψ∈Msg(L)¬ψ)
︸︷︷
︸
=:ψ
strict (q)
•ψLocInv
θ(q)=
∧
ℓ=(l,ι,φ
,l′,ι
′)∈LocInv,Θ(ℓ)=θ,ℓ
activeatqφ
Alo
cationl
iscalle
dfro
nt
locatio
no
fcu
tC
ifan
do
nly
if∄l ′∈L•l≺l ′.
Localin
variant(lo,ι
0,φ,l1,ι
1)
isactive
atcu
t(!)q
ifan
do
nly
ifl0
�l≺l1
for
som
efro
nt
locatio
nl
of
cutq
orl1
∈q∧ι1=
•.
•Msg(F
)=
{E
!xl,xl′|(l,E
,l ′)∈
Msg,l∈F}∪{E
?xl,xl′|(l,E
,l ′)∈
Msg,l ′∈F}
•xl∈X
isth
elo
gicalvariable
associate
dw
ithth
ein
stance
lineI
wh
ichin
clud
esl,i.e
.l∈I
.
•Msg(F
1,...,F
n)=
⋃
1≤i≤nMsg(Fi )
:C
1:C
2
x>
3
:C
3
ABC
DE
v=
0
Pro
gress
Co
nd
ition
– 18 – 2017-01-24 – Stbaconstr –
30
/6
6
ψhot
prog(q,qi )
=ψ
Msg(q
,qn)∧ψ
Cond
hot(q,qn)∧ψ
LocInv,•
hot
(qn)
•ψMsg(q
,qi )
=∧
ψ∈Msg(qi\q)ψ∧∧
j6=i
∧
ψ∈Msg(qj\q)\
Msg(qi\q)¬ψ
∧(stric
t=⇒
∧
ψ∈Msg(L)\
Msg(Fi)¬ψ)
︸︷︷
︸
=:ψ
strict (q,qi)
•ψCond
θ(q,qi )
=∧
γ=(L,φ
)∈Cond,Θ(γ)=θ,L∩(qi\q)6=
∅φ
•ψLocInv,•
θ(q,qi )
=∧
λ=(l,ι,φ
,l′,ι
′)∈LocInv,Θ(λ)=θ,λ•
-activeatqiφ
Localin
variant(l0,ι
0,φ,l1,ι
1)
is•
-activeatq
ifan
do
nly
if
•l0≺l≺l1
,or
•l=l0∧ι0=
•,o
r
•l=l1∧ι1=
•
for
som
efro
nt
locatio
nl
of
cut
(!)q
.
:C
1:C
2
x>
3
:C
3
ABC
DE
v=
0
Co
urse
Ma
p
– 18 – 2017-01-24 – main –
32
/6
6
UM
L
ModelInstances
NS
WE
CD
,SM
S=
(T,C,V
,atr),S
M
M=
(ΣDS,A
S,→
SM)
ϕ∈
OC
L
expr
CD
,SD
S,S
D
B=
(QSD,q
0 ,AS,→
SD,F
SD)
π=
(σ0 ,ε
0 )(cons0,Snd0)
−−−−−−−−→
u0
(σ1 ,ε
1 )···
wπ=
((σi ,co
nsi ,S
ndi ))
i∈N
G=
(N,E
,f)
Ma
them
atics
OD
UM
L
✔✔
✔✔
✔
✘
✔
✔
✔
✘
✘✔
✔
✔
✔
✔
Tell
Th
emW
ha
tYo
u’ve
To
ldT
hem
...
– 18 – 2017-01-24 – Sttwytt18 –
33
/6
6
•In
teractio
ns
canb
ere
flective
de
scriptio
ns
of
be
havio
ur,i.e
.
•d
escrib
ew
hat
be
havio
ur
is(u
n)d
esire
d,
with
ou
t(ye
t)de
finin
gh
ow
tore
aliseit.
•O
ne
visualfo
rmalism
for
inte
raction
s:Live
Se
qu
en
ceC
harts
•lo
cation
sin
diagram
ind
uce
ap
artialord
er,
•in
stantan
eo
us
and
ayn
chro
no
us
me
ssages,
•co
nd
ition
san
dlo
calinvarian
ts
•T
he
me
anin
go
fan
LS
Cis
de
fine
du
sing
TB
As.
•C
uts
be
com
estate
so
fth
eau
tom
aton
.
•Lo
cation
sin
du
cea
partialo
rde
ro
ncu
ts.
•A
uto
mato
n-tran
sition
san
dan
no
tation
sco
rresp
on
dto
asu
ccesso
rre
lation
on
cuts.
•A
nn
otatio
ns
use
sign
al/attrib
ute
exp
ressio
ns.
•L
ater:
•T
BA
have
Bü
chiacce
ptan
ce(o
fin
finite
wo
rds
(of
am
od
el)).
•Fu
llLSC
sem
antics.
•P
re-C
harts.
Excu
rsion
:B
üch
iA
uto
ma
ta
– 18 – 2017-01-24 – main –
34
/6
6
Fro
mF
inite
Au
tom
ata
toS
ymb
olic
Bü
chi
Au
tom
ata
– 18 – 2017-01-24 – Stba –
35
/6
6
q1
q2
01
A:
Σ=
{0,1}
q1
q2
01
B:
Σ=
{0,1}
q1
q2
01
1
0
B′:
Σ=
{0,1}
q1
q2
even(x
)
odd(x
)
Asym
:Σ
=({x}→
N)
q1
q2
even(x
)
odd(x
)
Bsym
:Σ
=({x}→
N)
Büch
i
infin
itew
ord
s
symb
olic
symb
olic
Büch
i
infin
itew
ord
s
Sym
bo
licB
üch
iA
uto
ma
ta
– 18 – 2017-01-24 – Stba –
36
/6
6
De
finitio
n.
AS
ym
bo
licB
üch
iAu
tom
aton
(TB
A)is
atu
ple
B=
(ExprB(X
),X,Q,qin
i ,→,Q
F)
wh
ere
•X
isa
set
of
logicalvariab
les,
•ExprB(X
)is
ase
to
fB
oo
lean
exp
ressio
ns
ove
rX
,
•Q
isa
finite
set
of
states,
•qin
i∈Q
isth
ein
itialstate,
•→
⊆Q
×ExprB(X
)×Q
isth
etran
sition
relatio
n.
Transitio
ns(q,ψ,q
′)fro
mq
toq′
arelab
elle
dw
ithan
exp
ressio
nψ
∈ExprB(X
).
•QF
⊆Q
isth
ese
to
ffair
(or
accep
ting
)states.
Wo
rd
– 18 – 2017-01-24 – Stba –
37
/6
6
De
finitio
n.Le
tX
be
ase
toflo
gicalvariable
san
dle
tExprB(X
)b
ea
seto
fBo
ole
ane
xpre
ssion
so
verX
.
Ase
t(Σ,·
|=··)
iscalle
dan
alph
abe
tfo
rExprB(X
)if
and
on
lyif
•fo
re
achσ∈
Σ,
•fo
re
ache
xpre
ssionexpr∈
ExprB
,and
•fo
re
achvalu
ationβ:X
→D(X
)o
flo
gicalvariable
s,
eith
er
σ|=βexpr
or
σ6|=βexpr.
(σsatisfie
s(o
rd
oe
sn
ot
satisfy)expr
un
de
rvalu
ationβ
)
An
infin
itese
qu
en
cew
=(σi )i∈
N0∈Σω
ove
r(Σ,·
|=··)
iscalle
dw
ord
(forExprB(X
)).
Ru
no
fT
BA
over
Wo
rd
– 18 – 2017-01-24 – Stba –
38
/6
6
De
finitio
n.Le
tB=
(ExprB(X
),X,Q,qin
i ,→,Q
F)
be
aT
BA
and
w=σ1,σ
2,σ
3,...
aw
ord
forExprB(X
).An
infin
itese
qu
en
ce
=q0,q
1,q
2,...
∈Qω
iscalle
dru
no
fB
ove
rw
un
de
rvalu
ationβ:X
→D(X
)if
and
on
lyif
•q0=qin
i ,
•fo
re
achi∈
N0
the
reis
atran
sition(qi ,ψ
i ,qi+
1)∈→
such
thatσi|=βψi .
Ru
no
fT
BA
over
Wo
rd
– 18 – 2017-01-24 – Stba –
38
/6
6
De
finitio
n.Le
tB=
(ExprB(X
),X,Q,qin
i ,→,Q
F)
be
aT
BA
and
w=σ1,σ
2,σ
3,...
aw
ord
forExprB(X
).An
infin
itese
qu
en
ce
=q0,q
1,q
2,...
∈Qω
iscalle
dru
no
fB
ove
rw
un
de
rvalu
ationβ:X
→D(X
)if
and
on
lyif
•q0=qin
i ,
•fo
re
achi∈
N0
the
reis
atran
sition(qi ,ψ
i ,qi+
1)∈→
such
thatσi|=βψi .
Exam
ple
:q1
q2
q1
even(x
)
odd(x
)
even(x
)
odd(x
)
Bsym
:Σ
=({x}→
N)
Th
eL
an
gu
age
of
aT
BA
– 18 – 2017-01-24 – Stba –
39
/6
6
De
finitio
n.
We
sayT
BAB=
(ExprB(X
),X,Q,q
ini ,→
,QF)
accep
tsth
ew
ord
w=
(σi )i∈
N0∈(E
xprB→
B)ω
ifan
do
nly
ifB
has
aru
n=
(qi )i∈
N0
ove
rw
such
that
fair(o
racce
ptin
g)state
sare
visited
infin
itely
ofte
nb
y
,i.e
.,such
that
∀i∈N
0∃j>i:qj∈QF.
We
callth
ese
tL(B
)⊆
(ExprB
→B)ω
of
wo
rds
that
areacce
pte
db
yB
the
lang
uage
ofB
.
Th
eL
an
gu
age
of
aT
BA
– 18 – 2017-01-24 – Stba –
39
/6
6
De
finitio
n.
We
sayT
BAB=
(ExprB(X
),X,Q,q
ini ,→
,QF)
accep
tsth
ew
ord
w=
(σi )i∈
N0∈(E
xprB→
B)ω
ifan
do
nly
ifB
has
aru
n=
(qi )i∈
N0
ove
rw
such
that
fair(o
racce
ptin
g)state
sare
visited
infin
itely
ofte
nb
y
,i.e
.,such
that
∀i∈N
0∃j>i:qj∈QF.
We
callth
ese
tL(B
)⊆
(ExprB
→B)ω
of
wo
rds
that
areacce
pte
db
yB
the
lang
uage
ofB
.
Exam
ple
:q1
q2
q1
even(x
)
odd(x
)
even(x
)
odd(x
)
Bsym
:Σ
=({x}→
N)
La
ng
uage
of
UM
LM
od
el
– 18 – 2017-01-24 – main –
40
/6
6
Th
eL
an
gu
age
of
aM
od
el
– 18 – 2017-01-24 – Smodellang –
41/
66
Re
call:AU
ML
mo
de
lM=
(C
D,S
M,O
D)
and
astru
cture
Dd
en
ote
ase
tJM
Ko
f(in
itialand
con
secu
tive) com
pu
tation
so
fth
efo
rm
(σ0,ε
0 )a0
−→
(σ1,ε
1 )a1
−→
(σ2,ε
2 )a2
−→...
wh
ere
ai=
(consi ,Sndi ,u
i )∈2
D(E)×
2(D
(E)∪
{∗,+
})×
D(C
)×
D(C)
︸︷︷
︸
=:A
.
Th
eL
an
gu
age
of
aM
od
el
– 18 – 2017-01-24 – Smodellang –
41/
66
Re
call:AU
ML
mo
de
lM=
(C
D,S
M,O
D)
and
astru
cture
Dd
en
ote
ase
tJM
Ko
f(in
itialand
con
secu
tive) com
pu
tation
so
fth
efo
rm
(σ0,ε
0 )a0
−→
(σ1,ε
1 )a1
−→
(σ2,ε
2 )a2
−→...
wh
ere
ai=
(consi ,Sndi ,u
i )∈2
D(E)×
2(D
(E)∪
{∗,+
})×
D(C
)×
D(C)
︸︷︷
︸
=:A
.
For
the
con
ne
ction
be
twe
en
mo
de
lsan
din
teractio
ns,w
ed
isreg
ardth
eco
nfigu
ration
of
the
eth
er ,an
dd
efin
eas
follo
ws:
De
finitio
n.
LetM
=(C
D,S
M,O
D)
be
aU
ML
mo
de
land
Da
structu
re.T
he
n
L(M
):=
{(σi ,u
i ,consi ,Sndi )i∈
N0∈
(ΣDS
×A)ω|
∃(εi )i∈
N0:(σ
0,ε
0)
(cons0,S
nd0)
−−−−−−−−−→
u0
(σ1,ε
1)···
∈JM
K}
isth
elan
gu
ageo
fM
.
Exa
mp
le:L
an
gu
age
of
aM
od
el
– 18 – 2017-01-24 – Smodellang –
42
/6
6
L(M
):=
{(σi ,u
i ,consi ,Sndi )i∈
N0|∃
(εi )i∈
N0:(σ
0,ε
0)
(cons0,S
nd0)
−−−−−−−−−→
u0
(σ1,ε
1)···
∈JM
K}
C1
C2
k:Int
C3
itsC2
0,1
itsC1
0,1
itsC3
0,1
CD
:
c1:C
1c2:C
2
k=
27
c3:C
3
itcC
1
itcC
2
itcC
3σ0 :
(σ,ε)
(cons,S
nd)
−−−−−−→
u···
→(σ
0,ε
0 )(cons0,S
nd0)
−−−−−−−−→
u0
(σ1,ε
1 )(cons1, {
(:E,c
2)}
)−−−−−−−−−−−→
c1
(σ2,ε
2 )( {
:E},S
nd2)
−−−−−−−−→
c2
(σ3 ,ε3 )
(cons3,{
(:F,c
3)}
)−−−−−−−−−−−→
c2
(σ4,ε
4 )(cons4,{
(G(),c
1)}
)−−−−−−−−−−−−→
c2
(σ5 ,ε5 )
({:F
},S
nd5)
−−−−−−−−→
c3
(σ6 ,ε6 )
→···
Wo
rds
over
Sig
na
ture
– 18 – 2017-01-24 – Smodellang –
43
/6
6
De
finitio
n.Le
tS
=(T,C,V,atr,E)
be
asign
ature
and
Da
structu
reo
fS
.
Aw
ord
ove
rS
and
Dis
anin
finite
seq
ue
nce
(σi ,u
i ,consi ,Sndi )i∈
N0∈Σ
DS×
D(C)×
2D
(E)×
2(D
(E)∪
{∗,+
})×
D(C
)
•T
he
langu
ageL(M
)o
fa
UM
Lm
od
elM
=(C
D,S
M,O
D)
isa
wo
rdo
ver
the
signatu
reS
(C
D)
ind
uce
db
yC
Dan
dD
,give
nstru
cture
D.
Sa
tisfactio
no
fS
ign
al
an
dA
ttribu
teE
xpressio
ns
– 18 – 2017-01-24 – Smodellang –
44
/6
6
•Le
t(σ,u,cons,Snd)∈
ΣDS
×A
be
atu
ple
con
sisting
of
syste
mstate
,ob
ject
ide
ntity
,con
sum
ese
t,and
sen
dse
t.
•Le
tβ:X
→D(C)
be
avalu
ation
of
the
logicalvariab
les.
Th
en
•(σ,u,cons,Snd)|=β
true
•(σ,u,cons,Snd)|=βψ
ifan
do
nly
ifIJψ
K(σ,β
)=
1
•(σ,u,cons,Snd)|=β¬ψ
ifan
do
nly
ifn
ot(σ,cons,Snd)|=βψ
•(σ,u,cons,Snd)|=βψ1∨ψ2
ifan
do
nly
if(σ,u,cons,Snd)|=βψ1
or(σ,u,cons,Snd)|=βψ2
•(σ,u,cons,Snd)|=βE
!x,y
ifan
do
nly
ifβ(x
)=u∧∃e∈
D(E
)•(e,β
(y))
∈Snd
•(σ,u,cons,Snd)|=βE
?x,y
ifan
do
nly
ifβ(y)=u∧cons⊂
D(E
)
Sa
tisfactio
no
fS
ign
al
an
dA
ttribu
teE
xpressio
ns
– 18 – 2017-01-24 – Smodellang –
44
/6
6
•Le
t(σ,u,cons,Snd)∈
ΣDS
×A
be
atu
ple
con
sisting
of
syste
mstate
,ob
ject
ide
ntity
,con
sum
ese
t,and
sen
dse
t.
•Le
tβ:X
→D(C)
be
avalu
ation
of
the
logicalvariab
les.
Th
en
•(σ,u,cons,Snd)|=β
true
•(σ,u,cons,Snd)|=βψ
ifan
do
nly
ifIJψ
K(σ,β
)=
1
•(σ,u,cons,Snd)|=β¬ψ
ifan
do
nly
ifn
ot(σ,cons,Snd)|=βψ
•(σ,u,cons,Snd)|=βψ1∨ψ2
ifan
do
nly
if(σ,u,cons,Snd)|=βψ1
or(σ,u,cons,Snd)|=βψ2
•(σ,u,cons,Snd)|=βE
!x,y
ifan
do
nly
ifβ(x
)=u∧∃e∈
D(E
)•(e,β
(y))
∈Snd
•(σ,u,cons,Snd)|=βE
?x,y
ifan
do
nly
ifβ(y)=u∧cons⊂
D(E
)
Ob
servatio
n:w
ed
on’t
use
allinfo
rmatio
nfro
mth
eco
mp
utatio
np
ath.
We
cou
ld,e
.g.,alsoke
ep
tracko
fe
ven
tid
en
tities
be
twe
en
sen
dan
dre
ceive
.
Exa
mp
le:M
od
elL
an
gu
age
an
dS
ign
al
/A
ttribu
teE
xpresio
ns
– 18 – 2017-01-24 – Smodellang –
45
/6
6
C1
C2
k:Int
C3
itsC2
0,1
itsC1
0,1
itsC3
0,1
CD
:
c1:C
1c2:C
2
k=
27
c3:C
3
itcC
1
itcC
2
itcC
3σ0 :
(σ,ε)
(cons,S
nd)
−−−−−−−→
u···
→(σ
0,ε
0)
(cons0,S
nd0)
−−−−−−−−−→
u0
(σ1,ε
1)
(cons1, {
(:E,c
2)}
)−−
−−−−−−−−−−→
c1
(σ2,ε
2)
({:E
},S
nd2)
−−−−−−−−→
c2
(σ3,ε
3)
(cons3, {
(:F,c
3)}
)−−−−−−−−−−−−→
c2
(σ4,ε
4)
(cons4, {
(G(),c
1)}
)−−−−−−−−−−−−−→
c2
(σ5,ε
5)
( {:F
},S
nd5)
−−−−−−−−→
c3
(σ6,ε
6)→
···
•β=
{x7→c1,y
7→c2,z
7→c3 }
•(σ
0 ,u0,cons0,S
nd0 )
|=βy.k>
0
•(σ
0 ,u0,cons0,S
nd0 )
|=βx.k>
0
•(σ
1 ,c1,cons1,{(:E,c
2 )})|=βE
!x,y
•(σ
1 ,c1,cons1,{(:E,c
2 )})|=βF
!x,y
•···
|=βE
?x,y
•W
ese
t(σ
4,c
2,cons4,{G(),c
1 })|=βGy,x!∧Gy,x?
(triggere
do
pe
ration
or
me
tho
dcall).
TB
Aover
Sig
na
ture
– 18 – 2017-01-24 – Smodellang –
46
/6
6
De
finitio
n.A
TB
A
B=
(ExprB(X
),X,Q,qin
i ,→,Q
F)
wh
ere
ExprB(X
)is
the
set
of
sign
alan
dattrib
ute
exp
ressio
nsExpr
S(E,X
)o
ver
signatu
reS
iscalle
dT
BA
ove
rS
.
TB
AC
on
structio
nP
rincip
le
– 18 – 2017-01-24 – Smodellang –
47
/6
6
Re
call:Th
eT
BAB(L
)o
fL
SC
Lis(E
xprB(X
),X,Q,q
ini ,→
,QF)
with
•Q
isth
ese
to
fcu
tso
fL
,qin
iis
the
instan
ceh
ead
scu
t,
•ExprB
=Φ
∪E!?(X
),
•→
con
sistso
flo
op
s,pro
gress
transitio
ns
(from F
),and
legale
xits(co
ldco
nd
./lo
calinv.),
•F
={C
∈Q
|Θ(C
)=
cold
∨C
=L}
isth
ese
to
fco
ldcu
ts.
So
inth
efo
llow
ing,w
e“o
nly”
ne
ed
toco
nstru
ctth
etran
sition
s’labe
ls:
→=
{(q,ψ
loop(q
),q)|q∈Q}∪
{(q,ψ
prog(q,q′),q′)
|q Fq′}
∪{(q,ψ
exit (q
),L)|q∈Q}
q...
ψloop(q
):“w
hat
allo
ws
us
tosta
yat
cutq”
“...F
1”
ψprog(q,q′):
“chara
cte
ris
atio
nof
fire
dsetFn”
ψexit (q
):“w
hatallo
ws
us
to
legally
exit”
true
:C
1:C
2
x>
3
:C
3
ABC
DE
v=
0
Co
urse
Ma
p
– 18 – 2017-01-24 – main –
48
/6
6
UM
L
ModelInstances
NS
WE
CD
,SM
S=
(T,C,V
,atr),S
M
M=
(ΣDS,A
S,→
SM)
ϕ∈
OC
L
expr
CD
,SD
S,S
D
B=
(QSD,q
0 ,AS,→
SD,F
SD)
π=
(σ0 ,ε
0 )(cons0,Snd0)
−−−−−−−−→
u0
(σ1 ,ε
1 )···
wπ=
((σi ,co
nsi ,S
ndi ))
i∈N
G=
(N,E
,f)
Ma
them
atics
OD
UM
L
✔✔
✔✔
✔
✔
✔
✔
✔
✔
✔✔
✔
✔
✔
✔
Live
Seq
uen
ceC
ha
rts—
Sem
an
ticsC
on
t’d
– 18 – 2017-01-24 – main –
49
/6
6
Fu
llL
SC
s
– 18 – 2017-01-24 – Slscsem –
50
/6
6
Afu
llLS
CL
=(((L
,�,∼
),I,Msg,Cond,LocIn
v,Θ
),ac0,am,Θ
L)
con
sistso
f
•b
od
y((L
,�,∼
),I,Msg,Cond,LocInv,Θ
),
•activatio
nco
nd
itionac0∈
Expr
S,
•strictn
ess
flagstric
t(if
false,
Lis
called
pe
rmissive
)
•activatio
nm
od
ea
m∈
{in
itial,invarian
t},
•ch
artm
od
ee
xisten
tial(Θ
L=
cold
)or
un
iversal(Θ
L=
hot).
Fu
llL
SC
s
– 18 – 2017-01-24 – Slscsem –
50
/6
6
Afu
llLS
CL
=(((L
,�,∼
),I,Msg,Cond,LocIn
v,Θ
),ac0,am,Θ
L)
con
sistso
f
•b
od
y((L
,�,∼
),I,Msg,Cond,LocInv,Θ
),
•activatio
nco
nd
itionac0∈
Expr
S,
•strictn
ess
flagstric
t(if
false,
Lis
called
pe
rmissive
)
•activatio
nm
od
ea
m∈
{in
itial,invarian
t},
•ch
artm
od
ee
xisten
tial(Θ
L=
cold
)or
un
iversal(Θ
L=
hot).
Co
ncre
tesy
ntax:
LS
C:
L1
AC
:ac0
AM
:in
itialI:
pe
rmissive
:C
1:C
2
φ
:C
3
E
F
G
Fu
llL
SC
s
– 18 – 2017-01-24 – Slscsem –
50
/6
6
Afu
llLS
CL
=(((L
,�,∼
),I,Msg,Cond,LocIn
v,Θ
),ac0,am,Θ
L)
con
sistso
f
•b
od
y((L
,�,∼
),I,Msg,Cond,LocInv,Θ
),
•activatio
nco
nd
itionac0∈
Expr
S,
•strictn
ess
flagstric
t(if
false,
Lis
called
pe
rmissive
)
•activatio
nm
od
ea
m∈
{in
itial,invarian
t},
•ch
artm
od
ee
xisten
tial(Θ
L=
cold
)or
un
iversal(Θ
L=
hot).
Ase
to
fw
ord
sW
⊆(E
xprB→
B)ω
isacce
pte
db
yL
ifan
do
nly
if
LS
C:
L1
AC
:ac1
AM
:in
itialI:
pe
rmissive
:C
1:C
2
φ
:C
3
E
F
G
ΘL
am
=in
itialam
=in
variant
cold
∃w
∈W
•w
0|=
ac∧¬ψexit (C
0)
∧w
0|=ψprog(∅,C
0)∧w/1∈
L(B
(L
))
∃w
∈W
∃k∈
N0•wk|=
ac∧¬ψexit (C
0)
∧wk|=ψprog(∅,C
0)∧w/k+
1∈
L(B
(L
))
hot
∀w
∈W
•w
0|=
ac∧¬ψexit (C
0)
=⇒
w0|=ψprog(∅,C
0)∧w/1∈
L(B
(L
))
∀w
∈W
∀k∈
N0•wk|=
ac∧¬ψexit (C
0)
=⇒
wk|=ψCond
hot
(∅,C
0)∧w/k+
1∈
L(B
(L
))
wh
ereC
0is
the
min
imal(o
rin
stance
he
ads)cu
t.
No
te:A
ctivatio
nC
on
ditio
n
– 18 – 2017-01-24 – Slscsem –
52
/6
6
LS
C:
L1
AC
:c1
AM
:in
itialI:
pe
rmissive
:C
1:C
2:C
3
E
F
GL
SC
:L
1A
M:
initial
I:p
erm
issive
:C
1:C
2:C
3
E
F
G
c1
Existen
tial
LS
CE
xam
ple:
Bu
yA
So
ftdrin
k
– 18 – 2017-01-24 – Sswlsc –
53
/6
6
LS
C:
bu
yso
ftdrin
kA
C:
trueA
M:
invarian
tI:
pe
rmissive
Use
rV
en
d.M
a.
E1
pSOFT
SOFT
Existen
tial
LS
CE
xam
ple:
Get
Ch
an
ge
– 18 – 2017-01-24 – Sswlsc –
54
/6
6
LS
C:
get
chan
geA
C:
trueA
M:
invarian
tI:
pe
rmissive
Use
rV
en
d.M
a.
C50
E1
pSOFT
SOFT
chg
-C50
TB
A-b
ased
Sem
an
ticso
fL
SC
s
– 18 – 2017-01-24 – Slscpresem –
55
/6
6
UM
L
ModelInstances
NS
WE
CD
,SM
S=
(T,C,V
,atr),S
M
M=
(ΣDS,A
S,→
SM)
ϕ∈
OC
L
expr
CD
,SD
S,S
D
B=
(QSD,q
0 ,AS,→
SD,F
SD)
π=
(σ0 ,ε
0 )(cons0,Snd0)
−−−−−−−−→
u0
(σ1 ,ε
1 )···
wπ=
((σi ,co
nsi ,S
ndi ))
i∈N
G=
(N,E
,f)
Ma
them
atics
OD
UM
L
✔✔
✔✔
✔
✘
✔
✘
✘✔
✔
✔
✔
✔
Plan
:
(i)G
iven
anL
SC
Lw
ithb
od
y((L,�,∼
),I,M
sg,C
ond,L
ocIn
v,Θ
),
(ii)co
nstru
cta
TB
AB
L,an
d
(iii)d
efin
elan
guage
L(L
)o
fL
inte
rms
ofL(B
L),
inp
articular
taking
activation
con
ditio
nan
dactivatio
nm
od
ein
toacco
un
t.
(iv)d
efin
elan
guage
L(M
)o
fa
UM
Lm
od
el.
•T
he
nM
|=L
(un
iversal)
ifan
do
nly
ifL(M
)⊆
L(L
).
An
dM
|=L
(existe
ntial)
ifan
do
nly
ifL(M
)∩L(L
)6=
∅.
Live
Seq
uen
ceC
ha
rts—
Prech
arts
– 18 – 2017-01-24 – main –
56
/6
6
Pre-C
ha
rts
– 18 – 2017-01-24 – Sprechart –
57
/6
6
LS
C:
bu
yw
ater
AC
:true
AM
:in
variant
I:strict
Use
rC
oinV
alidato
rcp
:Ch
oiceP
ane
lD
ispe
nse
r
C50
pWATER
cp->water
_in
_sto
ck
dWATER
OK
Afu
llLS
CL
=(P
C,MC,ac0,am,Θ
L)
actually
con
sisto
f
•p
re-ch
artPC
=((L
P,�
P,∼
P),I
P,S,MsgP,CondP,LocInvP,Θ
P)
(po
ssibly
em
pty),
•m
ain-ch
artMC
=((L
M,�
M,∼
M),I
M,S,MsgM,CondM,LocInvM,Θ
M)
(no
n-e
mp
ty),
•activatio
nco
nd
itionac0:Bool∈
Expr
S,
•strictn
ess
flagstric
t(o
the
rwise
called
pe
rmissive
)
•activatio
nm
od
ea
m∈
{in
itial,invarian
t},
•ch
artm
od
ee
xisten
tial(Θ
L=
cold
)or
un
iversal(Θ
L=
hot).
Pre-C
ha
rtsS
ema
ntics
– 18 – 2017-01-24 – Sprechart –
58
/6
6
LS
C:
bu
yw
ater
AC
:true
AM
:in
variant
I:strict
Use
rC
oinV
alidato
rcp
:Ch
oiceP
ane
lD
ispe
nse
r
C50
pWATER
cp->water
_in
_sto
ck
dWATER
OK
am
=in
itialam
=in
variant
ΘL = cold
∃w
∈W
∃m
∈N
0•
∧w
0|=
ac∧¬ψ
exit (C
P0)∧ψ
prog(∅,CP0)
∧w
1,...,wm
∈L(B
(PC))
∧wm
+1|=
¬ψ
exit (C
M0)
∧wm
+1|=ψ
prog(∅,CM0
)
∧w/m
+2∈
L(B
(MC))
∃w
∈W
∃k<m
∈N
0•
∧wk|=
ac∧¬ψ
exit (C
P0)∧ψ
prog(∅,CP0)
∧wk+
1,...,wm
∈L(B
(PC))
∧wm
+1|=
¬ψ
exit (C
M0)
∧wm
+1|=ψ
prog(∅,CM0
)
∧w/m
+2∈
L(B
(MC))
ΘL = hot
∀w
∈W
∀m
∈N
0•
∧w
0|=
ac∧¬ψ
exit (C
P0)∧ψ
prog(∅,CP0)
∧w
1,...,wm
∈L(B
(PC))
∧wm
+1|=
¬ψ
exit (C
M0)
=⇒
wm
+1|=ψ
prog(∅,CM0
)
∧w/m
+2∈
L(B
(MC))
∀w
∈W
∀k≤m
∈N
0•
∧wk|=
ac∧¬ψ
exit (C
P0)∧ψ
prog(∅,CP0)
∧wk+
1,...,wm
∈L(B
(PC))
∧wm
+1|=
¬ψ
exit (C
M0)
=⇒
wm
+1|=ψ
prog(∅,CM0
)
∧w/m
+2∈
L(B
(MC))
Un
iversal
LS
C:
Exa
mp
le
– 18 – 2017-01-24 – Sprechart –
59
/6
6
LS
C:
bu
yw
ater
AC
:true
AM
:in
variant
I:strict
Use
rC
oin
Valid
ator
cp:C
ho
iceP
ane
lD
ispe
nse
r
C50
pWATER
cp->water
_in
_sto
ck
dWATER
OK
Un
iversal
LS
C:
Exa
mp
le
– 18 – 2017-01-24 – Sprechart –
59
/6
6
LS
C:
bu
yw
ater
AC
:true
AM
:in
variant
I:strict
Use
rC
oin
Valid
ator
cp:C
ho
iceP
ane
lD
ispe
nse
r
C50
pWATER
¬(C
50!∨E1!∨pSOFT!
∨pTEA!∨pFIL
LUP!
cp->water
_in
_sto
ck
dWATER
OK
Un
iversal
LS
C:
Exa
mp
le
– 18 – 2017-01-24 – Sprechart –
59
/6
6
LS
C:
bu
yw
ater
AC
:true
AM
:in
variant
I:strict
Use
rC
oin
Valid
ator
cp:C
ho
iceP
ane
lD
ispe
nse
r
C50
pWATER
¬(C
50!∨E1!∨pSOFT!
∨pTEA!∨pFIL
LUP!
cp->water
_in
_sto
ck
dWATER
OK
¬(dSoft!
∨dTEA!)
Fo
rbid
den
Scen
ario
Exa
mp
le:D
on
’tG
iveTw
oD
rinks
– 18 – 2017-01-24 – Sprechart –
60
/6
6
Fo
rbid
den
Scen
ario
Exa
mp
le:D
on
’tG
iveTw
oD
rinks
– 18 – 2017-01-24 – Sprechart –
60
/6
6
LS
C:
on
lyo
ne
drin
kA
C:
trueA
M:
invarian
tI:
pe
rmissive
Use
rV
en
d.M
a.
E1
pSOFT
SOFT
SOFT
¬C50!∧¬E1!
false
No
te:S
equ
ence
Dia
gra
ms
an
d(A
ccepta
nce)
Test
– 18 – 2017-01-24 – Sprechart –
61/
66
LS
C:
bu
yso
ftdrin
kA
C:
trueA
M:
invarian
tI:
pe
rmissive
Use
rV
en
d.M
a.
E1
pSOFT
SOFT
LS
C:
get
chan
geA
C:
trueA
M:
invarian
tI:
pe
rmissive
Use
rV
en
d.M
a.
C50
E1
pSOFT
SOFT
chg
-C50
LS
C:
on
lyo
ne
drin
kA
C:
trueA
M:
invarian
tI:
pe
rmissive
Use
rV
en
d.M
a.
E1
pSOFT
SOFT
SOFT
¬C50!∧¬E1!
false
•E
xisten
tialLS
Cs∗
may
hin
tat
test-case
sfo
rth
eacce
ptan
cete
st!
(∗:as
we
llas(p
ositive)sce
nario
sin
gen
eral,like
use
-cases)
No
te:S
equ
ence
Dia
gra
ms
an
d(A
ccepta
nce)
Test
– 18 – 2017-01-24 – Sprechart –
61/
66
LS
C:
bu
yso
ftdrin
kA
C:
trueA
M:
invarian
tI:
pe
rmissive
Use
rV
en
d.M
a.
E1
pSOFT
SOFT
LS
C:
get
chan
geA
C:
trueA
M:
invarian
tI:
pe
rmissive
Use
rV
en
d.M
a.
C50
E1
pSOFT
SOFT
chg
-C50
LS
C:
on
lyo
ne
drin
kA
C:
trueA
M:
invarian
tI:
pe
rmissive
Use
rV
en
d.M
a.
E1
pSOFT
SOFT
SOFT
¬C50!∧¬E1!
false
•E
xisten
tialLS
Cs∗
may
hin
tat
test-case
sfo
rth
eacce
ptan
cete
st!
(∗:as
we
llas(p
ositive)sce
nario
sin
gen
eral,like
use
-cases)
•U
nive
rsalLS
Cs
(and
ne
gative/an
ti-scen
arios)in
gen
eraln
ee
de
xhau
stivean
alysis!
No
te:S
equ
ence
Dia
gra
ms
an
d(A
ccepta
nce)
Test
– 18 – 2017-01-24 – Sprechart –
61/
66
LS
C:
bu
yso
ftdrin
kA
C:
trueA
M:
invarian
tI:
pe
rmissive
Use
rV
en
d.M
a.
E1
pSOFT
SOFT
LS
C:
get
chan
geA
C:
trueA
M:
invarian
tI:
pe
rmissive
Use
rV
en
d.M
a.
C50
E1
pSOFT
SOFT
chg
-C50
LS
C:
on
lyo
ne
drin
kA
C:
trueA
M:
invarian
tI:
pe
rmissive
Use
rV
en
d.M
a.
E1
pSOFT
SOFT
SOFT
¬C50!∧¬E1!
false
•E
xisten
tialLS
Cs∗
may
hin
tat
test-case
sfo
rth
eacce
ptan
cete
st!
(∗:as
we
llas(p
ositive)sce
nario
sin
gen
eral,like
use
-cases)
•U
nive
rsalLS
Cs
(and
ne
gative/an
ti-scen
arios)in
gen
eraln
ee
de
xhau
stivean
alysis!
(Be
cause
the
yre
qu
ireth
atth
eso
ftware
ne
ver
eve
re
xhib
itsth
eu
nw
ante
db
eh
aviou
r.)
TB
A-b
ased
Sem
an
ticso
fL
SC
s
– 18 – 2017-01-24 – Slscpresem –
62
/6
6
UM
L
ModelInstances
NS
WE
CD
,SM
S=
(T,C,V
,atr),S
M
M=
(ΣDS,A
S,→
SM)
ϕ∈
OC
L
expr
CD
,SD
S,S
D
B=
(QSD,q
0 ,AS,→
SD,F
SD)
π=
(σ0 ,ε
0 )(cons0,Snd0)
−−−−−−−−→
u0
(σ1 ,ε
1 )···
wπ=
((σi ,co
nsi ,S
ndi ))
i∈N
G=
(N,E
,f)
Ma
them
atics
OD
UM
L
✔✔
✔✔
✔
✘
✔
✘
✘✔
✔
✔
✔
✔
Plan
:
(i)G
iven
anL
SC
Lw
ithb
od
y((L,�,∼
),I,M
sg,C
ond,L
ocIn
v,Θ
),
(ii)co
nstru
cta
TB
AB
L,an
d
(iii)d
efin
elan
guage
L(L
)o
fL
inte
rms
ofL(B
L),
inp
articular
taking
activation
con
ditio
nan
dactivatio
nm
od
ein
toacco
un
t.
(iv)d
efin
elan
guage
L(M
)o
fa
UM
Lm
od
el.
•T
he
nM
|=L
(un
iversal)
ifan
do
nly
ifL(M
)⊆
L(L
).
An
dM
|=L
(existe
ntial)
ifan
do
nly
ifL(M
)∩L(L
)6=
∅.
Co
urse
Ma
p
– 18 – 2017-01-24 – main –
63
/6
6
UM
L
ModelInstances
NS
WE
CD
,SM
S=
(T,C,V
,atr),S
M
M=
(ΣDS,A
S,→
SM)
ϕ∈
OC
L
expr
CD
,SD
S,S
D
B=
(QSD,q
0 ,AS,→
SD,F
SD)
π=
(σ0 ,ε
0 )(cons0,Snd0)
−−−−−−−−→
u0
(σ1 ,ε
1 )···
wπ=
((σi ,co
nsi ,S
ndi ))
i∈N
G=
(N,E
,f)
Ma
them
atics
OD
UM
L
✔✔
✔✔
✔
✘
✔
✔
✔
✘
✘✔
✔
✔
✔
✔
Tell
Th
emW
ha
tYo
u’ve
To
ldT
hem
...
– 18 – 2017-01-24 – Sttwytt19 –
64
/6
6
•B
üch
iauto
mata
accep
tin
finite
wo
rds
•if
the
ree
xistsis
aru
no
ver
the
wo
rd,
•w
hich
visitsan
accep
ting
statein
finite
lyo
ften
.
•T
he
lang
uage
of
am
od
elis
just
are
writin
go
fco
mp
utatio
ns
into
wo
rds
ove
ran
alph
abe
t.
•A
nL
SC
accep
tsa
wo
rd(o
fa
mo
de
l)if
Existe
ntial:
atle
asto
nw
ord
(of
the
mo
de
l)is
accep
ted
by
the
con
structe
dT
BA
,
Un
iversio
n:
allwo
rds
(of
the
mo
de
l)areacce
pte
d.
•A
ctivation
mo
de
initialactivate
sat
system
startup
(on
ly),in
variant
with
each
satisfied
activation
con
ditio
n(o
rp
re-ch
art).
•P
re-ch
artscan
be
use
dto
statefo
rbid
de
nsce
nario
s.
•S
eq
ue
nce
Diag
rams
canb
eu
sefu
lfor
testin
g.
Referen
ces
– 18 – 2017-01-24 – main –
65
/6
6
Referen
ces
– 18 – 2017-01-24 – main –
66
/6
6
Cran
e,M
.L.an
dD
inge
l,J.(20
07
).U
ML
vs.classicalvs.rhap
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charts:n
ot
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de
lsare
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de
qu
al.S
oftw
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ystems
Mo
delin
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m,W
.and
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l,D.(2
00
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athin
glife
into
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ssageS
eq
ue
nce
Ch
arts.Fo
rma
lMeth
od
sin
System
Design
,19(1):4
5–
80
.
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l,D.(19
97
).S
om
eth
ou
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on
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Gru
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.,ed
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prin
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l,D.an
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.(20
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:Mo
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diagram
s.S
oftw
are
an
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ystemM
od
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ar.(Early
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6,2
00
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p.13
-20
).
Hare
l,D.an
dM
arelly,R
.(20
03
).C
om
e,Let’sP
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cena
rio-B
ased
Pro
gram
min
gU
sing
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sa
nd
the
Pla
y-En
gine.
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ringe
r-Ve
rlag.
Klo
se,J.(2
00
3).LS
Cs:A
Gra
ph
icalFo
rma
lismfo
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eS
pecifica
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of
Co
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sis,Carlvo
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Un
iversität
Old
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rg.
OM
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7).
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ified
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age:S
up
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cture
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.1.2.
Tech
nicalR
ep
ort
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al/0
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.
OM
G(2
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ified
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frastructu
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rsion
2.4
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chn
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20
11-08
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.
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nifie
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od
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:Su
pe
rstructu
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rsion
2.4
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chn
icalRe
po
rtfo
rmal/
20
11-08
-06
.
Stö
rrle,H
.(20
03
).A
ssert,n
egate
and
refin
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en
tin
UM
L-2
inte
raction
s.In
Jürje
ns,J.,R
um
pe
,B.,Fran
ce,R
.,and
Fern
and
ez,E
.B.,e
dito
rs,CS
DU
ML
200
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um
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UM
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