Pruning Dynamic Slices

With Confidence

Xiangyu Zhang

Neelam Gupta

Rajiv Gupta

The University of Arizona

2

Dynamic Slicing

Dynamic slice is the set of statements that did affect the value of a variable at a program point for a specific program execution. [Korel and Laski, 1988]

……

10. A =

…...

20. B =

……

30. P =

31. If (P<0) {

......

35. A = A + 1

36. }

37. B=B+1

……

40. Error(A)

Dynamic Slice (A@40) = {10, 30, 31, 35, 40}Dynamic Slice (A@40) = {10, 30, 31, 35, 40}

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Effectiveness of Dynamic Slicing

Dynamic slicing is very effective in containing the faulty statement, however it usually produces over-sized slices -- [AADEBUG’05].

Problem:

How to automatically prune dynamic slices?

Approaches:• Coarse-grained pruning by intersecting multiple types

(backward, forward, bidirectional) of dynamic slices -- [ASE’05, ICSE’06]

• Fine-grained pruning of a backward slice by using confidence analysis -- this paper.

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Types of Evidence Used in Pruning

Buggy Execution

output_x

Classical dynamic slicing algorithms investigate bugs through the evidence of the wrong output

Critical Predicate [ICSE’06]

input0input_x

input2

output_x

predicate_x

output0

output1

predicate_x

Other types of evidence: Failure inducing input [ASE’05]

Partially correct output -- this paper

Benefits of more evidence Narrow the search for faulty stmt. Broaden the applicability

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Input

Output

Coarse-grained Pruning by Intersecting Slices

failure inducing input

BS

FS

FS(CP)BiS(CP)

++CP

BS^FS

6

Fine-grained Pruning by Exploiting Correct Outputs

……

10. A = 1 (Correct: A=3)

…...

20. B = A % 2

……

30. C = A + 2

……

40. Print (B)

41. Print (C)

Correct outputs produced in addition to wrong output.

BS(Owrong) – BS (Ocorrect) is problematic.

BS(C@41)= {10, 30, 41}

BS(B@40)= {10, 20, 40}

BS(C@41)-BS(B@40)

= {30,41}

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Confidence Analysis

Value produced at node n can reach only wrong output nodes

nn

There is no evidence that n is correct, so it should be in the pruned slice.

Should we include n in the slice?

??

Confidence(n)=0

Confidence(n)=?; 0 ≤ ? ≤ 1

Value produced at node n can reach both the correct and wrong output nodes.

nnnn

nn

Confidence(n)=1

Value produced at n can reach only correct outputs There is no evidence of incorrectness of n.

Therefore it cannot be in the slice.

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|)(|log1)( )|(| nAltnCf nrange

Confidence Analysis

nnnn

Range(n)={ a, b, c, d, e, f, g }

Alt(n)={ a }

Value(n) = a

Value(n) = bValue(n) = c

, c

• When |Alt(n)|==1, we have the highest confidence (=1) on the correctness of n;

• When |Alt(n)|==|Range(n)|, we have the lowest confidence (=0).

• |Range(n)| >= |Alt(n)|>=1

Alt(n) is a set of possible values of the variable defined by n, that when propagated through the dynamic dependence graph, produce the same values for correct outputs.

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Confidence Analysis: Example

……

10. A = ...

…...

20. B = A % 2

……

30. C = A + 2

……

40. Print (B)

41. Print (C) 0)41( Cf

1)40( Cf

0)30( Cf

1)20( Cf

2log2

|)(|log1)10( )|(|)|(| ArangeArange

ArangeCf

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Confidence Analysis: Two Problems

How to decide the Range of values for a node n?• Based on variable type (e.g., Integer).• Static range analysis.• Our choice:

Dynamic analysis based on value profiles. Range of values for a statement is the set of values defined by all of

the execution instances of the statement during the program run.

How to compute Alt(n)?• Consider the set of correct output values as constraints.• Compute Alt(n) by backward propagation of constraints

through the dynamic dependence subgraph corresponding to the slice.

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Computing Alt(n) Along Data Dependence

S1: T=... 9

S2: X=T+1 10 S3: Y=T%3 0

(X,T)= (6,5) (9,8)

(10,9)

(T,...)= (1,...) (3,...) (5,...) (8,...) (9,...)

(Y,T)=(0,3) (0,9) (1,1) (2,5) (2,8)

alt(T@S2)={9} alt(T@S3)={1,3,9}

alt(S1) = alt(T@S2) ∩ alt (T@S3) = {9}

alt(S2)={10} alt(S3)={0,1}

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Computing Alt(n) Along Control Dependence

S1: if (P) … True

S2: X=T+1 10 S3: Y=T%3 0

(X,T)= (6,5) (9,8)

(10,9)

(Y,T)=(0,3) (0,9) (1,1) (2,5) (2,8)

alt(S1) = {True}

alt(S2)={10} alt(S3)={0,1}

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Characteristics of Siemens Suite Programs

Program Description LOC Versions Tests

print_tokens Lexical analyzer 565 5 4072

print_tokens2 Lexical analyzer 510 5 4057

replace Pattern replacement 563 8 5542

schedule Priority scheduler 412 3 2627

schedule2 Priority scheduler 307 3 2683

gzip Unix utility 8009 1 1217

flex Unix utility 12418 8 525

• Each faulty version has a single manually injected error.• All the versions are not included:

No output is produced. Faulty statement is not contained in the backward slice.

• For each version three tests were selected.

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Results of Pruning

Program DS PDSmax PDSmax / DS PDSmin %Missed by PDSmin

print_tokens 110 35 31.8% 35 0%

print_tokens2 114 55 48.2% 55 0%

replace 131 60 45.8% 43 38.1%

schedule 117 70 59.8% 56 20%

schedule2 90 58 64.4% 50 0%

gzip 357 121 33.9% 10 100%

flex 727 27 3.7% 25 0%

On average, PDSmax = 41.1% of DS

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Confidence Based Prioritization

DD – dep. distance

CV – confidence values

Executed statement instances examined (%)

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The Potential of Confidence Analysis (1)

Case Study (replace v14)• 88 74 23

Dynamic SlicerWith Confidence

Pruned Slices

User Verified Statements as correct

Buggy Code

Input User

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The Potential of Confidence Analysis (2)

Relevant slicing (gzip v3 run r1)

Potential dep.Data dep.

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Conclusions

We have presented a new approach - Confidence analysis - that exploits the correct output values produced in an execution to prune the dynamic slice of an incorrect output.

We have developed a novel dynamic analysis based implementation of confidence analysis, which effectively pruned backward dynamic slices in our experiments.

• Pruned Slices = 41.1% Dynamic Slices, and still contain the faulty statement.

Our study shows that confidence analysis has additional applications beyond pruning – prioritization, interactive pruning & relevant slicing.

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The End