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Verification of CTL Properties of Hyperlinked Documents

Verification of CTL Properties of Hyperlinked Documents. APT Proposal 2005 Gordon J. Pace. What is CTL?. CTL = Computation Tree Logic Logic = A language to express properties Computation Tree = A description of a process which evolves over time, which may include non-determinism branching.

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Verification of CTL Properties of Hyperlinked Documents

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  1. Verification of CTL Properties of Hyperlinked Documents APT Proposal 2005 Gordon J. Pace

  2. What is CTL? • CTL = Computation Tree Logic • Logic = A language to express properties • Computation Tree = A description of a process which evolves over time, which may include non-determinism branching

  3. What is a computation tree?

  4. What is a computation tree? Each blobis a state of the system

  5. What is a computation tree? Each state may satisfy some basic propositions eg Deadlock

  6. What is a computation tree? Arrows indicate how states evolve over time

  7. What is a computation tree? Multiple outgoing arrows indicate different options exist

  8. What is CTL? CTL is a logic to describe properties of systems which evolve over time, enabling us to express things such as possibility and necessity.

  9. What does CTL look like? • AG P = along any execution path (A) property P holds everywhere/globally (G). • EF P =there exists an execution path (E) along which property P finally holds (F). • A (P U Q) = along any execution path (A) property P holds until property Q becomes true.

  10. What does CTL look like? Properties (ieP and Q) are CTL formulae themselves • AG P = along any execution path (A) property P holds everywhere/globally (G). • EF P =there exists an execution path (E) along which property P finally holds (F). • A (P U Q) = along any execution path (A) property P holds until property Q becomes true.

  11. What does CTL look like? Properties (eg P and Q) are CTL formulae themselves • AG P = along any execution path (A) property P holds everywhere/globally (G). • EF P =there exists an execution path (E) along which property P finally holds (F). • A (P U Q) = along any execution path (A) property P holds until property Q becomes true. Properties may also use standard logic operators (Æ, :, ), etc)

  12. CTL Examples • A state which satisfies the property atIndex is always reachable: AG (EF atIndex)

  13. CTL Examples • Once a state which satisfies cats is visited, states which satisfy dogs may only be reached via an index state: AG (cats ) A(:dogs U atIndex))

  14. CTL Examples • Once a state which satisfies cats is visited, states which satisfy dogs may only be reached via an index state: AG (cats ) A(:dogs U atIndex))

  15. But hyperdocuments are graphs

  16. But hyperdocuments are graphs with properties dogs cats dogs index cats dogs cats dogs

  17. Graphs to Trees • The spanning tree of a graph describes all possible paths in the graph.

  18. Graphs to Trees • The spanning tree of a graph describes all possible paths in the graph.

  19. The APT • Implement an algorithm to verify CTL properties • Implement a translator from an annotated collection of hyperlinked documents into a graph

  20. The APT • Implement an algorithm to verify CTL properties • Implement a translator from an annotated collection of hyperlinked documents into a graph • Given a collection of hyperlinked documents and a CTL property, we can verify the documents for consistency.

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