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Equivalence of open Petri nets

Equivalence of open Petri nets. Modeling and analysis with Petri net components. Marc Voorhoeve (AIS). Open net definition. Addition and comparison of bags. Global set of external places A. Open net: 6-tuple satisfying. External places. weighted arcs.

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Equivalence of open Petri nets

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  1. Equivalence of open Petri nets Modeling and analysis with Petri net components. Marc Voorhoeve (AIS)

  2. Open net definition Addition and comparison of bags Global set of external placesA Open net: 6-tuple satisfying

  3. External places weighted arcs Final marking indicators Transitions Open net model current int. marking b c r u Ö 2 p 2 q a Ö t v 2 Internal places

  4. Operational semantics Set of actions: external productions / consumptions / silent If Then Adding/removing external tokens Termination: Firing:  External tokens cannot be “seen”; only added and removed! Internal tokens can be neither seen nor added or removed.

  5. Example

  6. Properties State oriented (like ExSpect and RoseRT) Abstraction of internal actions. • Special case is OWF net • (used by Reisig e.a. for SOA definition) • initial source and final sink place • path property • WF nets: OWF nets without external places

  7. Interactionmodel (SOA) handover claim rdy offer

  8. Temporal predicates An active container can eventually become ready. offered but not readied yet #active: 0 1 2 rdy offer

  9. a a a c c b b c b Weak bisimilarity Relation between states, such that any sequence of additions and removals can be copied. Weakly bisimilar processes satisfy the same set of temporal predicates from a certain class. Production c after consumption a without b appearance is possible Nets not weakly bisimilar: bcan be removed after addition of an a Weakly bisimilar, not branching bisimilar! Always brief appearance of b after consumption a and before production c

  10. a Composition Hiding: Net: N c d b Hide b within N: Renaming: Rename c:

  11. a c Composition: merge + fusion Combine disjoint copies. Deadlock possible Fuse places with same name. No deadlock! a d b e c b

  12. Composition semantics Token transfer is possible!

  13. d a Compositional modeling Select open net subcomponents. Adapt interfaces by renaming and merge. Hide internal communication. e c b

  14. Congruence Weak bisimilarity is congruence w.r.t. operators Component with subcomponent C Replace C with weakly bisimilar C’ Resulting components remain weakly bisimilar. C’ C a b

  15. Caution with congruence Subnets at bottom are weakly bisimilar subcomponents. Hence the complete nets are weakly bisimilar too. External states differ! Left-hand net: b before c Weak bisimilarity is not a congruence for operators that directly access the state (inhibitor / reset arcs).

  16. Research opportunities Verification of properties based on structure of process Example: active container predicate. e C D b a active objects in X: offered (a) and not yet claimed (b) = sum of active objects in C and D State space reduction!

  17. The End

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