CTL Chapter 6 Part 2 Overview Review CTL Model Checking CTL - - PowerPoint PPT Presentation

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CTL Chapter 6 Part 2 Overview Review CTL Model Checking CTL - - PowerPoint PPT Presentation

Jun 01, 2023 326 likes •748 views

CTL Chapter 6 Part 2 Overview Review CTL Model Checking CTL model Checking algorithms for ( U ) Counter Examples and witnesses Symbolic Model Checking (Thursday) Binary Decision Trees

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CTL

Chapter 6 – Part 2

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Overview

  • Review CTL Model Checking
  • CTL model Checking algorithms for
  • ∃

(ɸ U )

  • ∃

□ɸ

  • Counter Examples and witnesses
  • Symbolic Model Checking (Thursday)
  • Binary Decision Trees
  • Encoding Transition Systems by Switching functions
  • Symbolic Computation
  • Ordered Binary Decision Diagrams
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Example parse tree for CTL

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∃ ◊((p=r)(p  q)) = ∃ (true U ((p=r)  (p  q)) ) Trace Algorithm on Whiteboard...

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Compute ∃ □q

Trace Algorithm on Whiteboard...

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Counter Examples and Witnesses

  • Counter Examples
  • Indicate the refutation of universally quantified path

formulae

  • Witness
  • Indicate the satisfaction of existentially quantified

path formulae

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Symbolic Model Checking

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Symbolic Model Checking

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Symbolic Model Checking

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Symbolic Model Checking

  • Encoding states and Transitions
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Symbolic Model Checking, ∃ (ɸ U )

  • Algorithm
  • Correction
  • Main operation in loop
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Symbolic Model Checking, ∃ (ɸ U )

∃ ◊((a=c)(a  b)) = ∃ (true U ((a=c)  (a  b)) ) Trace Algorithm with BDDs on Whiteboard... We need:

  • Sat(a),
  • Sat(b),
  • Sat(c),
  • Transitions (s,s')
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Symbolic Model Checking, ∃ □ɸ

  • Algorithm
  • Correction
  • Main operation in loop
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Symbolic Model Checking, ∃ □ɸ

∃ □ɸ Trace Algorithm with BDDs on Whiteboard... We need:

  • Sat(b),
  • Transitions (s,s')
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Symbolic Model Checking - ∃ □q

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BDT Cons...

  • May not have a data structure which is efficient for all

computations

  • Data structures which yield compact representations for

many computations that appear in practical applications

  • OBDDs - data structure that has been proven to be very successful

for model checking purposes

  • particularly in the area of hardware verification
  • Besides yielding compact representation for many “realistic”

transition systems, they enjoy the property that the Boolean connectives can be realized in time linear in the size of the input OBDDs

  • with appropriate implementation techniques, equivalence

checking can even be performed in constant time.

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BDT to OBDD

  • yield a data structure for computations that relies on a

compactification of binary decision trees.

  • skip redundant fragments of a binary decision tree.
  • This means collapsing constant subtrees (i.e., subtrees

where all terminal nodes have the same value) into a single node

  • identifying nodes with isomorphic subtrees
  • we obtain a directed acyclic graph of outdegree 2

– the inner nodes are labeled by variables and their

  • utgoing edges stand for the possible evaluations of

the corresponding variable.

– The terminal nodes are labeled by the function value.

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BDD to OBDD

  • Consider BDD
  • Correction: line from z3 to 0 should be a dashed line
  • To ODBBs
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BDD to OBDD

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Variable Ordering

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OBDD formal definition