Tutorial PETRI NETS 2006

1. Partner Generation for Petri Net Based Service Models Karsten Wolf (= Karsten Schmidt) Universität Rostock Open Workflow Nets

2. Wellformedness Workflow nets: Soundness - always possible to reach end state - every transition reachable open Workflow nets: There exist partner(s) such that - always possible to reach end state (Controllability) - every transition reachable (Transition covering)

4. Deciding centralized controllability Step 1: upper approximation of partner behaviour (  ,-) € C T B      oWFN can move partner can move both can move end state deadlock !€ !C !T (  ,C) (  ,€) , (  ,-) (  ,T) !T !€ (  ,CT) (  ,C€),(  ,C),(  ,-) , (  ,B) !€ ?B !T !C !T !C !€ ?B !C (  ,T€),(  ,T),(  ,-) , (  ,B) (  ,-) (  ,C€T),(  ,CT),(  ,T),(  ,C), (  ,T) (  ,C)

5. Deciding centralized controllability Step 2: remove bad states (  ,-) !T !€ (  ,CT) (  ,C€),(  ,C),(  ,-) , (  ,B) ?B !C !T !C !€ ?B (  ,T€),(  ,T),(  ,-) , (  ,B) (  ,-) € C T B      oWFN can move partner can move both can move end state deadlock !€ !C !T (  ,C) (  ,€) , (  ,-) (  ,T) !€ !T !C (  ,C€T),(  ,CT),(  ,T),(  ,C), (  ,T) (  ,C)

6. Deciding centralized controllability Step 3: iterate (  ,-) !€ (  ,C€),(  ,C),(  ,-) , (  ,B) ?B !C !T !€ ?B (  ,T€),(  ,T),(  ,-) , (  ,B) (  ,-) € C T B      oWFN can move partner can move both can move end state deadlock !€ !C !T (  ,C) (  ,€) , (  ,-) (  ,T) !T (  ,CT) !C

7. Deciding centralized controllability Step 4: (optional): construct oWFN (  ,-) !€ (  ,C€),(  ,C),(  ,-) , (  ,B) ?B !C !T !€ ?B (  ,T€),(  ,T),(  ,-) , (  ,B) (  ,-) € C T B      !€ !C !T (  ,C) (  ,€) , (  ,-) (  ,T) € C T B

11. Example for a reduction rule I  Do not send messages that cannot be consumed in the future of at least one state Preserves most permissive partner

12. Example for a reduction rule II Do not send anything as long as you can receive something Does not preserve most permissive partner !b

13. Decentralized partner generation traced back to centralized case: C 1 ... C n  C 1 || ... || C n Approach: as central case, but remove - bad states - states where actions belonging to different parties are not commutative Algorithm is nondeterministic

14. Example a b   !b !a !a 1. !b 2.

16. Autonomous partner generation a b  ? not possible in this example

22. Excluding „ I do not want tea!“ Remove nodes containing T (  ,-) !€ !C (  ,C) (  ,€) , (  ,-) !€ (  ,C€),(  ,C),(  ,-) , (  ,B) ?B !C (  ,-) € C T B      !T (  ,T) !T !€ ?B (  ,T€),(  ,T),(  ,-) , (  ,B)

24. Enforcing „ I want coffee!“ Step 2: split Undecided states (  ,-) (  ,C) (  ,€) , (  ,-) (  ,T) !€ (  ,C€),(  ,C),(  ,-) , (  ,B) ?B !C !T !€ ?B (  ,T€),(  ,T),(  ,-) , (  ,B) (  ,-) € C T B      !€ !C !T

25. Enforcing „ I want coffee!“ Step 3: Remove unsuccessful end states (  ,-) (  ,C) (  ,€) , (  ,-) (  ,T) !€ (  ,C€),(  ,C),(  ,-) , (  ,B) ?B !C !T !€ (  ,T€),(  ,T),(  ,-) , (  ,B) (  ,-) € C T B      !€ !C !T ?B (  ,-)

26. Enforcing „ I want coffee!“ Step 4: Generate partner (  ,-) !€ !C (  ,C) (  ,€) , (  ,-) !€ (  ,C€),(  ,C),(  ,-) , (  ,B) ?B !C (  ,-) € C T B      !T (  ,T) !T !€ (  ,T€),(  ,T),(  ,-) , (  ,B)

27. Synchronous interaction  Simultaneous occurrence relevant (irrelevant in asynchronous case) Otherwise, same algorithms applicable

29. Justification of construction (centralized partner)   K(q) = { m | [m,q] reachable in composed system} … remember construction …

32. Properties of partners II a b c      a  b   ac  bc  c  a b c   b   bc  c  a b c  a  c not knowledge-aware knowledge-aware P w.r.t. N knowlegde-aware iff removing all but one incoming edges does not change K(q)

35. Ad 2. mb ka  mb ka kd Idea: merge states q, q‘ with K(q) = K(q‘) a b c     ,  a   b,  ,  a   c,   ,  a   b,  ,  a  c,  a b a c c a b a Not knowledge driven Knowledge-driven

38. Example ! ? ? !  