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

What is a computation tree?

What is a computation tree?

Each blob is a state of

the system

What is a computation tree?

Each state may satisfy some basic

propositions eg Deadlock

What is a computation tree?

Arrows indicate how states evolve

over time

What is a computation tree?

Multiple outgoing arrows indicate different

options exist

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.

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.

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.

Properties (ie P and Q) are CTL

formulae themselves

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.

Properties (eg P and Q) are CTL

formulae themselves

Properties may also use standard logic operators

(Æ, :, ), etc)

CTL Examples

A state which satisfies the property atIndex is always reachable:

AG (EF atIndex)

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))

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))

But hyperdocuments are graphs

index cats dogs

dogs

cats dogs

cats

dogs

But hyperdocuments are graphswith properties

Graphs to Trees

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

Graphs to Trees

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

The APT

Implement an algorithm to verify CTL properties

Implement a translator from an annotated collection of hyperlinked documents into a graph

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.