Shoupon Lin Advisor Nicholas F Maxemchuk Department of Electrical Engineering Columbia University New York NY 10027 Problem Markov decision process or Markov chain with exceedingly large state space ID: 431791
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Probabilistic Model Checking of Systems with a Large State Space: A Stratified Approach
Shou-pon
Lin
Advisor: Nicholas F.
Maxemchuk
Department
of
Electrical
Engineering,
Columbia
University,
New
York,
NY
10027
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Problem: Markov decision process or Markov chain with exceedingly large state spaceCheck if the
Markov decision process or Markov
chain satisfies a given probabilistic safety propertySolution: Not completely traverse all states, but prioritize state traversal on those states that are more likely to be reached during system execution; stop when using up all the memoryCompute probability bound by considering the uncertainty contributed by unexplored states
Model checking probabilistic system
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Probabilistic safety propertiesA probabilistic safety property combines a regular safety property and a probability bound between 0 and 1
For all adversary , the probability for to satisfy should be greater than or equal to
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Reachability analysisNormally it can be done by taking the product , find the set of acceptance states , and solve a linear program to find
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Discretized levels of probabilistic choicesGiven a layering parameter ,
probabilistic choices are categorized into several discretization
levelsIf level-0 (high probability choices)If level-1 low probability choicesIf
level-2
low probability
choices
etc.
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Stratified traversalAssign discretized levels to probabilistic transitions
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Stratified traversalPrioritize traversal of more probable states
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Stratified traversalPrioritize traversal of more probable states
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Stratified traversalPrioritize traversal of more probable states
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Stratified traversalThe unexplored states are the less likely ones to be reached during system execution
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Stratified traversalThe unexplored states are the less likely ones to be reached during system execution
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Determine if the property holdsLet
Suppose the procedure stops when finishing layer kIf , holdsIf , is violatedOtherwise, whether holds or not is uncertain12Slide13
Determine if the property holdsLet
Suppose the procedure stops when finishing layer kIf , holdsIf , is violatedOtherwise, whether holds or not is uncertain13Slide14
Preliminary resultsWe applied stratified
verification to
the lock protocol that resolves conflicting reqs in our automobile application.Stratified method is able to compute the upper-bound of error probability while PRISM terminates when running out of memory
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Future worksFeasibility of integrating this method into currently available model checkers and state-of-art techniques
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Future worksFeasibility of integrating this method into currently available model checkers and state-of-art techniques
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Thank you for your attention!Contact: shouponlin@ee.columbia.eduSlide17
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Thank you for your attention!
Contact: shouponlin@ee.columbia.edu