Lecture 18: Live Sequence Charts II
16
– 18 – 2017-01-24 – main – Software Design, Modelling and Analysis in UML Lecture 18: Live Sequence Charts II 2017-01-24 Prof. Dr. Andreas Podelski, Dr. Bernd Westphal Albert-Ludwigs-Universität Freiburg, Germany Content – 18 – 2017-01-24 – Scontent – 2/66 • Reflective Descriptions of Behaviour • Interactions • A Brief History of Sequence Diagrams • Live Sequence Charts • Abstract Syntax, Well-Formedness • Semantics • TBA Construction for LSC Body • Cuts, Firedsets • Signal / Attribute Expressions • Loop / Progress Conditions • Excursion: Büchi Automata • Language of a Model • Full LSCs • Existential and Universal • Pre-Charts • Forbidden Scenarios • LSCs and Tests The Plan – 18 – 2017-01-24 – Splan – 3/66 6.B 7.A 7.B • Thu, 19. 1.: Live Sequence Charts I • Firstly: State-Machines Rest, Code Generation • Tue, 24. 1.: Live Sequence Charts II • Thu, 26. 1.: Live Sequence Charts III • • • Tue, 31. 1.: Tutorial 7 • • Thu, 2. 2.: Model Based/Driven SW Engineering • • Mon, 6. 2.: Inheritance • Tue, 7. 2.: Meta-Modelling + Questions February, 17th: The Exam. Constructive Behavioural Modelling in UML: Discussion – 18 – 2017-01-24 – main – 4/66 Semantic Variation Points – 18 – 2017-01-24 – Ssemvar – 5/66 Pessimistic view: There are too many... • For instance, • allow absence of initial pseudo-states object may then “be” in enclosing state without being in any substate; or assume one of the children states non-deterministically • (implicitly) enforce determinism, e.g. by considering the order in which things have been added to the CASE tool’s repository, or some graphical order (left to right, top to bottom) • allow true concurrency • etc. etc. Exercise: Search the standard for “semantical variation point”. • Crane and Dingel (2007), e.g., provide an in-depth comparison of Statemate, UML, and Rhapsody state machines — the bottom line is: • the intersection is not empty (i.e. some diagrams mean the same to all three communities) • none is the subset of another (i.e. each pair of communities has diagrams meaning different things) Optimistic view: • tools exist with complete and consistent code generation. • good modelling-guidelines can contribute to avoiding misunderstandings. Reflective Descriptions of Behaviour – 18 – 2017-01-24 – main – 6/66
Transcript of Lecture 18: Live Sequence Charts II
– 18 – 2017-01-24 – main –
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– 18 – 2017-01-24 – Scontent –
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66
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– 18 – 2017-01-24 – Sinteract –
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– 18 – 2017-01-24 – Sinteract –
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66
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– 18 – 2017-01-24 – main –
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;
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
sod
ystate
charts:n
ot
allmo
de
lsare
create
de
qu
al.S
oftw
are
an
dS
ystems
Mo
delin
g,6(4
):415
–4
35
.
Dam
m,W
.and
Hare
l,D.(2
00
1).L
SC
s:Bre
athin
glife
into
Me
ssageS
eq
ue
nce
Ch
arts.Fo
rma
lMeth
od
sin
System
Design
,19(1):4
5–
80
.
Hare
l,D.(19
97
).S
om
eth
ou
ghts
on
statech
arts,13ye
arslate
r.In
Gru
mb
erg,O
.,ed
itor,C
AV
,volu
me
125
4o
fLN
CS
,page
s2
26
–2
31.S
prin
ger-V
erlag.
Hare
l,D.an
dM
aoz,S
.(20
07
).A
ssert
and
ne
gatere
visited
:Mo
dalse
man
ticsfo
rU
ML
seq
ue
nce
diagram
s.S
oftw
are
an
dS
ystemM
od
eling
(SoS
yM).
Toap
pe
ar.(Early
versio
nin
SC
ES
M’0
6,2
00
6,p
p.13
-20
).
Hare
l,D.an
dM
arelly,R
.(20
03
).C
om
e,Let’sP
lay:S
cena
rio-B
ased
Pro
gram
min
gU
sing
LSC
sa
nd
the
Pla
y-En
gine.
Sp
ringe
r-Ve
rlag.
Klo
se,J.(2
00
3).LS
Cs:A
Gra
ph
icalFo
rma
lismfo
rth
eS
pecifica
tion
of
Co
mm
unica
tion
Beh
avio
r.P
hD
the
sis,Carlvo
nO
ssietzky
Un
iversität
Old
en
bu
rg.
OM
G(2
00
7).
Un
ified
mo
de
ling
langu
age:S
up
erstru
cture
,versio
n2
.1.2.
Tech
nicalR
ep
ort
form
al/0
7-11-02
.
OM
G(2
011a).
Un
ified
mo
de
ling
langu
age:In
frastructu
re,ve
rsion
2.4
.1.Te
chn
icalRe
po
rtfo
rmal/
20
11-08
-05
.
OM
G(2
011b
).U
nifie
dm
od
elin
glan
guage
:Su
pe
rstructu
re,ve
rsion
2.4
.1.Te
chn
icalRe
po
rtfo
rmal/
20
11-08
-06
.
Stö
rrle,H
.(20
03
).A
ssert,n
egate
and
refin
em
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
3,n
um
be
rT
UM
-I03
23
.Tech
nisch
eU
nive
rsitätM
ün
che
n.
