Diagnosability Verification with Parallel LTL-X Model Checking Based on Petri Net Unfoldings

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Diagnosability Verification with Parallel LTL-X
Model Checking Based on Petri Net Unfoldings
Agnes Madalinski1, and Victor Khomenko2 1Faculty
of Engineering Science, University Austral de
Chile 2School of Computing Science, Newcastle
University, UK
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Outline

• Concept of fault diagnosis and diagnosability
• Diagnosability verification with LTL-X model
  checking
• Experimental result
• Conclusions and future work

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Concept of fault diagnosis
observations
system
actions (repair, reconfigure)
faults
detection, localisation and identification of
faults

• diagnosis task of explaining abnormal behaviours
  of a system given observations about its behaviour

• diagnosability the possibility of detecting
  faults by monitoring the visible behaviour of the
  system

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Diagnosability
observations
system
o1, o2, o3, o4 ,o5
fault occurred?

• A system is diagnosable if an occurrence of a
  fault can be detected with certainty in a bounded
  time.

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Diagnosability
aaXcdacYddeaaZcc
XYZ
ccaXdYfadeaaaZee

• For a system with finite state space
• absence of two infinite traces having the same
  observable traces one having a fault and the
  other not having one

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System model

• labelled Petri net N (P,T?,M0,O,U,l)?
• O set of observable transition labels
• U set of unobservable transition labels
• l T ? O ? U
• F ? U set of fault transition labels

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Fault tracking
f
fault tracking net Nft for state based LTL-X
model checking
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Verifier

• sync. product of two replicas of Nft on
  observable transitions
• a trace in verifier represents a pair of traces
  of Nft with the same projection on observable
  transitions

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Expressing non-diagnosability in LTL-X

• eventually pf1 is marked (fault occures in Nft1)
• pf2 always stays marked (no fault in Nft2)

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Simplifying the verifier
f2 must never fire
enforced by removing the transitions f2 and f2
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Simplifying the verifier
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Unfolding Approach to LTL-X Model-Checking

• Net system is constructed as composition of
• verifier and
• the Büchi automaton accepting diag
• Efficient Petri net unfolding based LTL-X model
  checking
• Relies on the partial order view of concurrent
  computation
• Represents states implicitly, using an acyclic
  net
• Esparza and Heljanko (ICALP 2000, SPIN 2001)
• Parallel LTL-X model-checker for high level Petri
  nets by Schröter and Khomenko (CAV 2004),
  implemented in PUNF tool

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Tools used for experiments

• PComp to compute the verifier
• PUNF parallel LTL-X model checker
• Available at
• http//homepages.cs.ncl.ac.uk/victor.khomenko/tool
  s/tools.html

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Experiments assorted benchmarks
diagnosable
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Experiments scalable pipelines (non-diag.)
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Experiments scalable pipelines (diag.)
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Experiments parallel mode
16,777,216 upper bound on the number of states of
the verifier
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Conclusions

• Experimental results show that the method works
  quite well, especially on highly concurrent
  systems
• A good level of parallelisation has been achieved
• However the benchmarks are rather artificial
• Larger and more practical benchmarks are needed
• Proposed approach can be trivialy generalised to
  high-level Petri nets

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