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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
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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
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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
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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}
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Relationship diagram
Coloured PNs
unfolding
Low-level prefixColoured prefix
unfolding
Low-level PNsexpansion
?
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~
Relationship diagram
Coloured PNs
unfolding
Low-level prefixColoured prefix
unfolding
Low-level PNsexpansion
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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]
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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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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)