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## PowerPoint Slideshow about ' Application of TBDs' - farren

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Application of TBDs

Technical development

Ordered TBDs

Operations on ordered TBDs (,,)

Reduced ordered TBDs

Model checking == Manipulation of TBDs

Abstraction

An abstraction of a TBD on a label u

=

Conjunction of

a simplication on –u and a simplication on u

Simplification on a Label u/-u

A

- B

- B

- C

A

- C

- D

- D

- D

D

- A

Select all non-terminal nodes labeled with singed/unsignedu

Replace the selected nodes with a simpler one according to given rules

Abstraction on u

Given a TBD.

(1) Make a simplification on –u and a simplification on u

(2) Make a conjunction of the two simplifications

u

z

Quantified Boolean Formulas

Consider formulas with variables p1,p2,…,pn

pi

φ

φΨ

x. φ

pi

s

s

- x

t

s

- pn+1

pn+1

pn+1

φ is valid comp( ) holds

s

Reduced Ordered TBDs

u

x

y

- pn+1

Not allowed

x

- pn+1

pn+1

x

pn+1

- pn+1

y

pn+1

y

pn+1

x

x

y

Non-terminal

x

y

y

y

pn+1

y

x

y

x>0

Reduction Rules for -u

- u

- u

- z

- T

z

- z

z

T

T

- - z

z

- z

z

T

T

- T’

T’

T

z

T’

T

- T’

T

z

T’

T

- u

u

z

- T

z

- z

- T

z

T

- z

z

- T

- z

z

Explanation on Some Rules (1)

u

- u

u

~x

~y

- z

- z

- z

- x

- y

z

- x

- y

x

- y

z

x

- y

- x

y

z

- x

y

x

y

z

x

y

Explanation on Some Rules (2)

u

- u

u

~x

~y

- z

- z

- z

- x

- y

z

- x

- y

x

- y

z

x

- y

- x

y

z

- x

y

x

y

z

x

y

Boolean Diagram Model Checking

m variables for representing states

2m variables for representing transitions

Let n=2m

Construct a TBD for the formula representing the initial states

Construct a TBD for the formula representing the transition relation

The rest follows from the CTL model checking techniques

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