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

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

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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

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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

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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?

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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

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

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

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

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

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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

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

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

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

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15 bMSC Decomposition Exemple m1 m2 m3 a m4 m5 b

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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

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

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

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

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20 Normalisation of HMSCs Caution when Shifting bMSCs! M3 M2 M1 M3 M2 M1 M2 Even if I(M1) I(m3)=

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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

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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

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

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