1 Decomposition of Message Sequence Charts Loïc Hélouët, Pierre Le Maigat SAM 2000

2 Outline n Motivations n bMSC Decomposition n Normalisation of HMSCs n Conclusion

3 Motivations Time Analysis & Granularity M1 M2 M1’ M2 M1’’ No finite time model: Reduce the language or Consider bMSCs as the granularity of the method

4 Motivations Equivalence C c AB AB B C m2 m3 m1 A B C c m2 m3 A B C c m1 A B C m2 m3  

5 bMSC Decomposition bMSC Independance I(M1)  I(M2)=   M1;M2  M2;M1  M1  M2 M1 M2 m1 AB bMSC M1 CD bMSC M2 M1 M2 m2 M2 M1    Decomposition?

6 bMSC Decomposition How to Split a bMSC ? A B m1 A B Preserve messages A B m1 Preserve coregions A B m1 A B 

7 bMSC Decomposition AB m1 m2 Message Crossing can not be separated AB m1 m2 C But may involve all instances ! m3

8 bMSC Decomposition Cutting points A B m1 m2 C a1 a2

9 bMSC Decomposition Cuts A B m1 m2 C m3 C1 C2 C3

10 bMSC Decomposition Valid Cuts A B m1 m2 C m3 C1 C2 C3

11 bMSC Decomposition Basic patterns Sets of events that are not partitionned by valid cuts A B m1 m2 C m3 a B1 B2 B3  B1 B2 B3

12 bMSC Decomposition G(M) AB m1 m2 G(M) = Order relation on events + Cycles between pairs of events that must not be separated

13 bMSC Decomposition Basic patterns are the strongly connected components of G(M)  Use Tarjan ’s algorithm

14 bMSC Decomposition Exemple A B m1 m2 C m3 a m4 m5 b

15 bMSC Decomposition Exemple m1 m2 m3 a m4 m5 b

16 bMSC Decomposition Exemple A a B m1 C A B m2 b B C m3 m4 A B m5 bMSC M1 bMSC M2 bMSC M3 bMSC M4 bMSC M5  M1M2 M3 M4 M5

17 Normalisation of HMSCs M1 M2 M5 M6 M7 M3 M4 HMSC = bMSC Automata Generate local sequencing of bMSC Decomposition ? Normal form ?

18 Normalisation of HMSCs  M1M2  M1M3  M2 M3 M1 Factorisation  M2M3  Lift Up M1  M1M3 M2 If I(M1)  I(m3)= 

19 Normalisation of HMSCs Caution when factorizing bMSCs!  M2M3  M2M4  M3 M4 M2 M1 M3 M4 M2 M1  Preserve cycles

20 Normalisation of HMSCs Caution when Shifting bMSCs!  M3 M2 M1 M3 M2 M1 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 H n = Hn+1

22 Normalisation of HMSCs M1 M2 M5 M6 M7 M1 1 M2 M5 2 M6 M7  M3 M4 M1 2 M1 3 M4 M3 1  M3 2 M5 1 Factorize Lift UP

23 Conclusion n for analysis (time, concurrency,…) n as an equivalence Decomposition: