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

Motivation

Low-level PNs: Can be efficiently

verified Not convenient

for modelling

High-level descriptions:

Convenient for modelling

Verification is hard

Gap

Coloured PNs:a good intermediate formalism

5

Coloured PNs

1 2

w<u+v

vu

w

{1,2} {1,2}

{1..4}

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Expansion

1 2

w<u+v

vu

w

{1,2} {1,2}

{1..4}

The expansion faithfully models the original net

Blow up in size

7

Unfolding

1 2

w<u+v

vu

w

{1,2} {1,2}

{1..4}

1 2

u=1v=2w=1

1

u=1v=2w=2

2

8

Example: computing GCD

3 2

2 1

1 0

1

u=3, v=2

u=2, v=1

u=1

v0m n

v

u%v

u

v

0u

u

{0..100}{0..100}

{0..100}

9

Relationship diagram

Coloured PNs

unfolding

Low-level prefixColoured prefix

unfolding

Low-level PNsexpansion

?

10

~

Relationship diagram

Coloured PNs

unfolding

Low-level prefixColoured prefix

unfolding

Low-level PNsexpansion

11

Relationship diagram1 2

w<u+v

vu

w

{1,2} {1,2}

{1..4}

1 2

u=1v=2w=1

1 2

u=1v=2w=2

12

Relationship diagram

Coloured PNs

unfolding

Prefix

unfolding

Low-level PNsexpansion

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

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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

Extensions: infinite place types

v0m n

v

u%v

u

v

0u

u

{0..100}{0..100}

{0..100}

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Extensions: infinite place types

v0m n

v

u%v

u

v

0u

u

N N

N

3 2

2 1

1 0

1

u=3, v=2

u=2, v=1

u=1

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Extensions: infinite place types

v0m n

v

u%v

u

v

0u

u

3 2

2 1

1 0

1

u=3, v=2

u=2, v=1

u=1

{0..2}{1..3}

{1}

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Refined expansion

Coloured PNs

unfolding

Prefix

unfolding

Low-level PNsexpansion

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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.)