Branching Processes of HighLevel Petri Nets Victor Khomenko

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 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Refined expansion Low-level PNs Coloured PNs unfolding Prefix 18

Experimental results J Tremendous improvements for colourintensive PNs (e. g. GCD) J Negligible slow-down (<0. 5%) for controlintensive PNs (e. g. Lamport’s mutual exclusion algorithm) 19

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