Effective Slicing

1

• Effective Slicing

Anne Mulhern Computer Sciences Department Universi
ty of Wisconsin-Madison Madison, WI
USA mulhern_at_cs.wisc.edu www.cs.wisc.edu/mulhern
2
Two Correct Dynamic Slices
full slice n ? 1
read(n)


if (n 1)
x 3



?x
full slice n ? 2


y 2



if (y 2)
x 2
?x
program
read(n)
x 1
y 2
if (n 1)
x 3
y 1
if (y 2)
x 2
?x
?
?
3
Union of Slices is Incorrect
full slice n ? 1,2
read(n)

y 2
if (n 1)
x 3

if (y 2)
x 2
?x
program
read(n)
x 1
y 2
if (n 1)
x 3
y 1
if (y 2)
x 2
?x
n p/s x p/s y p/s
? 1 ? ? ?
? 1 1/ ? ?
? 1 1/ ? 2 ?
? ?
? 1 3 2 ?
? 1 3 1/2
?
1 3/2 1/2 ?
3/2
4
Why is This a Problem?

• Given a set of inputs that cause program failure
• Want the correct slice for all failures
• Given a flag that takes multiple values
• Want the correct slice for whenever the flag is
  set, regardless of its value

5
Two Correct Relevant Slices
relevant slice n ? 2
read(n)

y 2
if (n 1)


if (y 2)
x 2
?x
relevant slice n ? 1
read(n)


if (n 1)
x 3
y 1
if (y 2)

?x
program
read(n)
x 1
y 2
if (n 1)
x 3
y 1
if (y 2)
x 2
?x
?
?
6
Union of Relevant Slices is Correct
relevant slice n ? 1,2
read(n)

y 2
if (n 1)
x 3
y 1
if (y 2)
x 2
?x
program
read(n)
x 1
y 2
if (n 1)
x 3
y 1
if (y 2)
x 2
?x
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We Can Slice Twice

• If we take the union of slices as our program and
  slice again on the same inputs
• we may get a smaller program
• Example the union of relevant slices for inputs
  2 and 3

8
Fixpoint Computation
relevant slice n ? 3


y 2



if (y 2)
x 2
?x
relevant slice n ? 2


y 2



if (y 2)
x 2
?x
relevant slice n ? 2,3
read(n)

y 2
if (n 1)


if (y 2)
x 2
?x
?
?
So long as n in 2,3 choice of n is unimportant
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Effective Slicing

• Dynamic slicing algorithms - two arguments
• P - the program
• s - the initial state
• Effective slicing algorithm - an additional
  argument
• ?? - the nodes to consider when calculating
  potential dependence
• effective(P, s, Ø ) full(P, s)
• effective(P, s, P) relevant(P, s)

10
Effective Slicing for Approximation

• Potential dependence need only be taken into
  account when the potential statement is in the
  union of slices
• Choose ?? to be all nodes in the union of
  execution slices

11
Two Correct Effective Slices
effective slice n ? 3


y 2



if (y 2)
x 2
?x
effective slice n ? 2


y 2



if (y 2)
x 2
?x
program
read(n)
x 1
y 2
if (n 1)
x 3
y 1
if (y 2)
x 2
?x
?
?
12
Summary

• Unions of relevant slices are correct
• Take into account potential dependences
• Relevant slicing can be used in a fixpoint
  computation
• Semantic information can be extracted from the
  result
• Effective slicing generalizes full and relevant
  slicing
• Possibly potential statements are an explicit
  parameter
• Effective slicing can be used to find an
  approximation of the fixpoint

13
Future Work

• Theoretical
• How many steps to reach fixpoint?
• Practical
• How big are unions of relevant slices?
• How good an approximation can effective slicing
  give?
• How many dynamic semantic facts can be extracted?
• eg., what choices of initial state are irrelevant
  for this subset?

14

• Effective Slicing

Anne Mulhern Computer Sciences Department Universi
ty of Wisconsin-Madison Madison, WI
USA mulhern_at_cs.wisc.edu www.cs.wisc.edu/mulhern