Decomposition of Message Sequence Charts

1
Decomposition ofMessage Sequence Charts
Loïc Hélouët, Pierre Le Maigat
SAM 2000
2
Outline

• Motivations
• bMSC Decomposition
• Normalisation of HMSCs
• Conclusion

3
Motivations

• Time Analysis Granularity

No finite time model Reduce the
language or Consider bMSCs as the granularity of
the method
M1
M1
M2
4
Motivations

• Equivalence

A
B
C
m1
c
m1
c
A
B
C
m1
?
A
B
c
A
m2
B
C
?
m3
m3
m2
m2
B
m3
5
bMSC Decomposition

• bMSC Independance
• I(M1) ? I(M2)? ? M1M2 ? M2M1 ? M1?? M2

bMSC M1
m1
A
B
?
M2
?
M1
??
bMSC M2
C
D
m2
Decomposition?
6
bMSC Decomposition

• How to Split a bMSC ?

Preserve messages
B
A
m1
B
A
m1
Preserve coregions
?
7
bMSC Decomposition
Message Crossing can not be separated
A
B
C
m1
m2
But may involve all instances !
m3
8
bMSC Decomposition

• Cutting points

9
bMSC Decomposition
Cuts
10
bMSC Decomposition
Valid Cuts
11
bMSC Decomposition
Basic patterns Sets of events that are not
partitionned by valid cuts
B
A
C
B1
B2
a
m1
B2
??
B1
B3
m2
m3
B3
12
bMSC Decomposition
G(M)
G(M) Order relation on events Cycles
between pairs of events that must not be
separated
A
B
m1
m2
13
bMSC Decomposition
Basic patterns are the strongly connected
components of G(M) ? Use Tarjan s
algorithm
14
bMSC Decomposition
Exemple
B
A
C
m1
a
m2
m4
m3
b
m5
15
bMSC Decomposition
Exemple
m1
a
m2
b
m4
m3
m5
16
bMSC Decomposition
Exemple
bMSC M1
bMSC M3
bMSC M2
bMSC M4
bMSC M5
17
Normalisation of HMSCs

• HMSC bMSC Automata
• Generate local sequencing
• of bMSC
• Decomposition ?
• Normal form ?

18
Normalisation of HMSCs
Factorisation
M1
?
??
M1
M2
??
M1
M3
M2
M3
Lift Up
M1
??
M1
M3
If I(M1) ? I(m3)?
?
??
M2
M3
M2
19
Normalisation of HMSCs
Caution when factorizing bMSCs!
M1
M2
?
M1
M3
M4
??
M2
M3
??
M2
M4
M1
?
M2
Preserve cycles
M3
M4
20
Normalisation of HMSCs
Caution when Shifting bMSCs!
M1
??
M2
M1
?
M3
M2
M3
M2
Even if I(M1) ? I(m3)?
21
Normalisation of HMSCs
Let H be a HMSC Algorithm Split all bMSCs of H
into Basic Patterns Repeat Factorize
(H) Lift(H) Until Hn Hn1
22
Normalisation of HMSCs
??
M12
M11
M1
Lift UP
M2
Factorize
M5
M6
M3
M6
??
M51
M32
M31
M7
M4
M7
M52
M4
23
Conclusion
Decomposition

• for analysis (time, concurrency,)
• as an equivalence

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