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Branching Processes of High-Level Petri Nets

Branching Processes of High-Level Petri Nets. Victor Khomenko and Maciej Koutny University of Newcastle upon Tyne. Talk Outline. Motivation Unfoldings of coloured PNs Relationship between HL and LL unfoldings Extensions Future work. Petri net unfoldings. Partial-order semantics of PNs

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Branching Processes of High-Level Petri Nets

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  1. Branching Processes of High-Level Petri Nets Victor Khomenko and Maciej Koutny University of Newcastle upon Tyne

  2. Talk Outline • Motivation • Unfoldings of coloured PNs • Relationship between HL and LL unfoldings • Extensions • Future work

  3. Petri net unfoldings • Partial-order semantics of PNs • Alleviate the state space explosion problem • Efficient model checking algorithms • Low-level PNs are not convenient for modelling

  4. ColouredPNs: a good intermediate formalism Gap Motivation Low-level PNs: • Can be efficiently verified • Not convenient for modelling High-level descriptions: • Convenient for modelling • Verification is hard

  5. {1,2} {1,2} 1 2 u v w<u+v w {1..4} Coloured PNs

  6. {1,2} {1,2} 1 2   u v w<u+v w {1..4} Expansion • The expansion faithfully models the original net • Blow up in size

  7. {1,2} {1,2} 1 2 u v 1 2 w<u+v w u=1 v=2 w=1 u=1 v=2 w=2 {1..4} 1 2 Unfolding

  8. 2 3 {0..100} {0..100} v0 u%v v u=3, v=2 m n u v 2 1 u 0 u=2, v=1 u 1 0 {0..100} u=1 1 Example: computing GCD

  9. expansion Low-level PNs unfolding unfolding Low-level prefix Coloured prefix Relationship diagram Coloured PNs ?

  10. expansion Low-level PNs unfolding unfolding Low-level prefix Coloured prefix Relationship diagram Coloured PNs ~

  11. {1,2} {1,2} 1 2   u v w<u+v w {1..4} 1 2 u=1 v=2 w=1 u=1 v=2 w=2 1 2 Relationship diagram

  12. expansion Low-level PNs Relationship diagram Coloured PNs unfolding unfolding Prefix

  13. Benefits • Avoiding an exponential blow up when building the expansion • Definitions are similar to those for LL unfoldings, no new proofs • All results and verification techniques for LL unfoldings are still applicable • Canonicity, completeness and finiteness results • Model checking algorithms

  14. Benefits • Existing unfolding algorithms for LL PNs can easily be adapted • Usability of the total adequate order proposed in [ERV’96] • All the heuristics improving the efficiency can be employed (e.g. concurrency relation and preset trees) • Parallel unfolding algorithm [HKK’02]

  15. {0..100} {0..100} v0 u%v v m n u v u 0 u {0..100} Extensions: infinite place types

  16. 2 3 N N v0 u%v v u=3, v=2 m n u v 2 1 u 0 u=2, v=1 u 1 0 N u=1 1 Extensions: infinite place types

  17. 2 3 {1..3} {0..2} v0 u%v v u=3, v=2 m n u v 2 1 u 0 u=2, v=1 u 1 0 {1} u=1 1 Extensions: infinite place types

  18. expansion Low-level PNs Refined expansion Coloured PNs unfolding unfolding Prefix

  19. Experimental results • Tremendous improvements for colour-intensive PNs (e.g. GCD) • Negligible slow-down (<0.5%) for control-intensive PNs (e.g. Lamport’s mutual exclusion algorithm)

  20. Future Work Partial-order verification for other PN classes (nets with read/inhibitor arcs, priorities etc.)

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