Verification of CTL Properties of Hyperlinked Documents

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 blob is a state of the system
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What is a computation tree?
Each state may satisfy some basic propositions eg
Deadlock
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What is a computation tree?
Arrows indicate how states evolve over time
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What is a computation tree?
Multiple outgoing arrows indicate different
options exist
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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.

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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 (ie 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.

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)
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CTL Examples

• A state which satisfies the property atIndex is
  always reachable
• AG (EF atIndex)

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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))

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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))

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But hyperdocuments are graphs
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But hyperdocuments are graphs
with properties
dogs
cats dogs
index
cats dogs
cats
dogs
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Graphs to Trees

• The spanning tree of a graph describes all
  possible paths in the graph.

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Graphs to Trees

• The spanning tree of a graph describes all
  possible paths in the graph.

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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.