Branching Processes of High-Level Petri Nets

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Branching Processes of High-Level Petri Nets

• Victor Khomenko and Maciej Koutny
• University of Newcastle upon Tyne

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Talk Outline

• Motivation
• Unfoldings of coloured PNs
• Relationship between HL and LL unfoldings
• Extensions
• Future work

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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

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Coloured PNs
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Expansion

• The expansion faithfully models the original net
• Blow up in size

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Unfolding
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Example computing GCD
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Relationship diagram
Coloured PNs
?
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Relationship diagram
Coloured PNs

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Relationship diagram
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Relationship diagram
Coloured PNs
unfolding
unfolding
Prefix
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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 ERV96
• All the heuristics improving the efficiency can
  be employed (e.g. concurrency relation and preset
  trees)
• Parallel unfolding algorithm HKK02

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Extensions infinite place types
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Extensions infinite place types
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Extensions infinite place types
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Refined expansion
Coloured PNs
unfolding
unfolding
Prefix
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Experimental results

• Tremendous improvements for colour-intensive PNs
  (e.g. GCD)
• Negligible slow-down (lt0.5) for
  control-intensive PNs (e.g. Lamports mutual
  exclusion algorithm)

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Future Work

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