This document discusses using symbolic reasoning and dynamic symbolic execution to help with program debugging, repair, and regression testing. It presents an approach where inputs are grouped based on producing the same symbolic output to more efficiently test programs and debug issues. Relevant slice conditions are computed to precisely capture input-output relationships and group related paths. This technique aims to find a notion of "similarity" between inputs and executions that is coarser than just considering program paths. The approach is demonstrated on example programs and shown to reduce debugging time compared to only considering program paths.

1. Abhik Roychoudhury
National University of Singapore
ISSTA 2013 Workshop - July 2013
1
HOW SYMBOLIC REASONING CAN
HELP PROGRAM (DEBUGGING AND)
REPAIR

2. DEBUGGING VS. BUG HUNTING
P
input = 0
output = 0
P
G( pc = end output > input)
Model Checker
Counter-example:
input = 0, output = 0
We should have (output >
input)
(a) Debugging (b) Model Checking
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3. EXECUTION WITH SYMBOLIC INPUTS
3
out = in + 1 out = in * 2
Program P Program
Q
Symbolic input
in ==
Concrete output
out == + 1
Concrete output
out == 2*
To expose difference, try to find such that + 1 2 *
Symbolic input
in ==
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4. PATH CONDITION COMPUTATION
4
1 input in;
2 z = 0; x = 0;
3 if (in > 0){
4 z = in *2;
5 x = in +2;
6 x = x + 2;
7 }
8 else …
9 if ( z > x){
return error;
}
in == 5
Line# Assignment store Path condition
1 {} true
2 {(z,0),(x,0)} true
3 {(z,0),(x,0)} in > 0
4 {(z,2*in), (x,0)} in > 0
5 {(z,2*in), (x,in+2)} in > 0
6 {(z,2*in), (x, in+4)} in > 0
7 {(z, 2*in), (x, in+4)} in > 0
9 {(z, 2*in), (x, in+4)} in>0 (2*in > in +4)
Using the assignment store, can also compute symbolic
expression for output along each path.
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5. USAGE OF DSE
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input x, y;
a = 0; b = 0;
if (x > y)
a = x;
else
a = y;
if (x + y > 10)
b = a;
return b;
Passing inputs: Continue the search for
failing inputs, those which do not go through
the “same” path.
Path condition of (x == 0, y == 0)
x ≤ y x + y ≤ 10
x == 0, y == 0
x > y
a = x a = y
x +y >10
b = a
return b
Cover more paths
x ≤ y x + y ≤ 10
x ≤ y x + y ≤ 10
x ≤ y

6. IMPLICIT ASSUMPTION IN DSE
 Inputs executing a path are “similar”.
 If we test one of them, no need to test the others.
 Use “similarity” to skip over parts of a large search
space.
 DSE is a tool to achieve this goal.
 Testing is search over paths, not search over inputs.
 Coarser-grained notion of similarity?
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7. THE SEARCH FOR “SIMILARITY”
 Testing
 No need to test “similar” inputs.
 Can look for “similarity” beyond paths.
 Debugging
 Given a failing input – find “similar” inputs that pass
 Logical comparison to detect “deviations” – bug report.
 Repair
 Find “similar” inputs showing the “same” error
 Group all executions through which a fail is rescued.
 Symbolic execution used to capture “intended behavior”.
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8. 8
“SIMILARITY” BEYOND PATHS
1 int x,y,z; // input variables
2 int out; // output variable
3 int a;
4 int b = 2;
5 if(x - y > 0) //b1
6 a = x;
7 else
8 a = y;
9 if (x + y > 10) //b2
10 b = a;
11 if(z*z > 3) //b3
12 printf("square(z) > 3 n");
13 else
14 printf("square(z) <= 3 n");
15 out = b; //slicing criteria
If x − y > 0 and x + y > 10,
then out == x
Paths: 1,2,3,4,5,6,9,10,11,12,15
1,2,3,4,5,6,9,10,11,13,14,15
If x − y ≤ 0 and x + y > 10,
then out == y
Paths: 1,2,3,4,5,7,8,9,10,11,12,15
1,2,3,4,5,7,8,9,10,11,13,14,15
If x + y ≤ 10,
then out == 2
Paths: 1,2,3,4,5,6,9,11,12,15
1,2,3,4,5,6,9,11,13,14,15
1,2,3,4,5,7,8,9,11,12,15
1,2,3,4,5,7,8,9,11,13,14,15
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9. PROGRAM SUMMARY
9
¬(x+y >10) (out== 2)
(x-y > 0) (x+y > 10) (out == x)
¬(x-y > 0) (x+y > 10) (out == y)
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Group inputs which produce the same symbolic output.
- Efficient testing, and debugging

10. RELEVANT SLICE CONDITION
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1 int x,y,z; //input variables
2 int out; // output variable
3 int a;
4 int b = 2;
5 if(x - y > 0) //b1
6 a = x;
7 else
8 a = y;
9 if (x + y > 10) //b2
10 b = a;
11 if(z*z > 3) //b3
12 printf("square(z)>3 n");
13 else
14 printf("square(z)<=3n");
15 out = b; //slicing criteria
Relevant Slicing
Potential Dependence
 Path condition computed over
relevant slice
 Backward dynamic slicing
 control,
 data and
 potential dependence.
 Precisely captures i-o relationship
 Groups several paths together

11. PROPERTIES
t, t’ program inputs
π(t): execution trace of input t
RSC(π(t)): relevant slice condition computed on π(t)
 Same symbolic output:
 Given a path π(t), if an input t’ satisfies RSC(π(t)), then
RSC(π(t’) is the same as RSC(π(t)). π(t) and π(t’)
computes the same symbolic output.
 Complete RSC coverage:
 Path exploration (based on reordered RSC) can explore all
symbolic outputs.
11
Property for Path Condition:
Suppose is a path condition,
if t’ satisfy , , then the path condition for
contains as a prefix.
)...( 21 i )'(t
)...( 21 i
However, this does NOT hold for Relevant-Slice Condition, making the
exploration completely out of order.
mi
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)...( 21 mf

12. (EXPECTED) VALIDATION
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0
100
200
300
400
500
Relevant Slice
Condition
Paths explored Average formula size
0
50000
100000
150000
200000 Relevant Slice
Condition

13. REGRESSION DEBUGGING
Old Stable
Program P
Test Input t
New Buggy
Program P’
1
3
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14. ADAPTING TRACE COMPARISON
Directly Compare σ and π
Old Stable
Program P
Test Input t
New Buggy
Program P’
Path σ
for t
Path π
for t
New Input t’
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15. THE SEARCH FOR “SIMILARITY”
Old
Pgm. P
New
Pgm. P’
Buggy input
The new test input
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16. DARWIN
f:Path condition
of t in P
Old Stable
Program P
Test Input t
New Buggy
Program P’
Alternative Input t’
Concrete and
Symbolic Execution
STP Solver
and input
validation
Satisfiable sub-
formulae from
f f’
f':Path condition
of t in P’
'ff
Bug Report (Assembly level)
Bug Report (Source level)
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17. CHOOSING ALTERNATIVE INPUTS
b1
b6
b3
b2
b4
b5
11
2
3
4
5
2
3

)...(' 21 mf
1f
21f
321f

'Solve ff
'f At most m alternate inputs !!
Check for satisfiability of

1
7

18. BUG REPORT COMPUTATION
b1
b6
b3
b2
b4
b5
1
2
3
4
5
3

'f 321f
tnew = input obtained by solving
Bug report by comparing traces of tbug
and tnew should be the branch b3 !!
At most m alternate inputs
at most m lines in bug report.
tbug
tnew
18
)...(' 21 mf
'Solve ff
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19. COARSER-GRAINED “SIMILARITY”
Old
Pgm. P
New
Pgm. P’
Buggy input
The new test input
19
Solve rsc rsc’ instead of f f ’
rsc, rsc’ Relevant slice conditions
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20. RESULTS ON DARWIN20
Programs Path Condition
Relevant Slice
Condition
Time
JLex 543min 15min
Jtopas 81min 5min
NanoXML 3min 43s
Results
JLex 50LOC 3LOC
Jtopas 4LOC 4LOC
NanoXML 8LOC 6LOC
Less time
Better result
Smaller formula to solve, Less formula to solve ->
More accurate bug report, obtained faster.
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21. IF WE ARE INTERESTED IN STATISTICS
 Jlex
 ~7290 LoC
 v1.2.1 vs. v1.1.1
 Diff == 518 LoC
 Jtopas
 ~5754 LoC
 v0.7 vs. v0.8
 Diff == 2489 LoC
 NanoXML
 ~5244 LoC
 v2.1 vs. v2.2
 Diff == 2496 LoC 21
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Other results in DARWIN paper
First implementation on top of
BitBlaze (thanks to BitBlaze team)
Results on
libPNG – 36K LoC
TCPflow – 1000 LoC
Different implementations of
web-servers
Miniweb, Savant against Apache.

22. PROGRAM REPAIR
 Correctness specification Test suite
 Program repair Passing all tests
 Repair strategy Rescue failing executions
 Use of symbolic execution
 Group together all executions through which a failing execution
could be rescued.
 New notion of “similarity”
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23. 0. THE PROBLEM
1 int is_upward( int inhibit, int up_sep, int down_sep){
2 int bias;
3 if (inhibit)
4 bias = down_sep; // bias= up_sep + 100
5 else bias = up_sep ;
6 if (bias > down_sep)
7 return 1;
8 else return 0;
9 }
inhibit up_sep down_se
p
Observed
output
Expected
Output
Result
1 0 100 0 0 pass
1 11 110 0 1 fail
0 100 50 1 1 pass
1 -20 60 0 1 fail
0 0 10 0 0 pass
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24. 1. FIND A SUSPECT
1 int is_upward( int inhibit, int up_sep, int down_sep){
2 int bias;
3 if (inhibit)
4 bias = down_sep; // bias= up_sep + 100
5 else bias = up_sep ;
6 if (bias > down_sep)
7 return 1;
8 else return 0;
9 }
Line Score Rank
4 0.75 1
8 0.6 2
3 0.5 3
6 0.5 3
5 0 5
7 0 5
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25. 2 WHAT IT SHOULD HAVE BEEN
1 int is_upward( int inhibit, int up_sep, int down_sep){
2 int bias;
3 if (inhibit)
4 bias = down_sep; // bias= up_sep + 100
5 else bias = up_sep ;
6 if (bias > down_sep)
7 return 1;
8 else return 0;
9 }
inhibit up_sep down_se
p
Observed
output
Expected
Output
Result
1 11 110 0 1 fail
inhibit = 1, up_sep = 11, down_sep = 110
bias = X, path condition = true
inhibit = 1, up_sep = 11, down_sep = 110
bias = X, path condition = X> 110
inhibit = 1, up_sep = 11, down_sep = 110
bias = X, path condition = X ≤ 110
Line 4
Line 7 Line 8
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26. 2. WHAT IT SHOULD HAVE BEEN
1 int is_upward( int inhibit, int up_sep, int
down_sep){
2 int bias;
3 if (inhibit)
4 bias = f(inhibit, up_sep, down_sep)
5 else bias = up_sep ;
6 if (bias > down_sep)
7 return 1;
8 else return 0;
9 }
Inhibit
== 1
up_sep
== 11
down_se
p == 110
Symbolic Execution
f(1,11,110) > 110
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27. 3. FIX THE SUSPECT
 Accumulated constraints
 f(1,11, 110) > 110
 f(1,0,100) ≤ 100
 …
 Find a f satisfying this constraint
 By fixing the set of operators appearing in f
 Candidate methods
 Search over the space of expressions
 Program synthesis with fixed set of operators
 More efficient!!
 Generated fix
 f(inhibit,up_sep,down_sep) = up_sep + 100
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28. TO RECAPITULATE
 Ranked Bug report
 Hypothesize the error causes – suspect
 Symbolic execution
 Specification of the suspicious statement
 Input-output requirements from each test
 Repair constraint
 Program synthesis
 Decide operators which can appear in the fix
 Generate a fixed statement by solving repair constraint.
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29. WHAT IT SHOULD HAVE BEEN
Buggy Program
…
var = a + b – c;x
Concrete test input
Concrete Execution
Symbolic Execution with x as the
only unknown
Path conditions,
Output Expressions
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30. EXAMPLE
30
1 int is_upward( int inhibit, int up_sep, int down_sep){
2 int bias;
3 if (inhibit)
4 bias = f(inhibit, up_sep, down_sep) // X
5 else bias = up_sep ;
6 if (bias > down_sep)
7 return 1;
8 else return 0;
9 }
Inhibit == 1 up_sep == 11 down_sep == 110
Symbolic Execution
( pcj outj == expected_out(t) )
f(t) == X
j Paths
Repair constraint
( (X >110 1 ==1)
(X ≤ 110 0 == 1)
)
f(1,11,110) == X
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31. TO RECAPITULATE
 Ranked Bug report
 Hypothesize the error causes – suspect
 Symbolic execution
 Specification of the suspicious statement
 Input-output requirements from each test
 Repair constraint
 Program synthesis
 Decide operators which can appear in the fix
 Generate a fix by solving repair constraint.
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32. WHY PROGRAM SYNTHESIS
 Instead of solving
 Select primitive components to be used by the synthesized program
based on complexity
 Look for a program that uses only these primitive components and
satisfy the repair constraint
 Where to place each component?
 What are the parameters?
int tmp = down_sep -1;
return up_sep + tmp;
int tmp=down_sep + 1;
return tmp- inhibit;
int tmp = down_sep -1;
return tmp + inhibit ;
int tmp = down_sep -1;
return tmp + inhibit ;
+
+
inhibit up_sep
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Repair Constraint:
f(1,11,110) > 110 f(1,0,100) ≤ 100
f(1,-20,60) > 60
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33. LOCATION VARIABLES
 Define location variables for each component
 Constraint on location variables solved by SMT.
 Well-formed e.g. defined before being used
 Output constraint from each test (repair constraint)
 Meaning of the components
 Lines determine the value Lx == Ly x == y
 Once locations are found, program is constructed.
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Components = {+}
Lin == 0, Lout == 1, Lout+ == 1, Lin1+ == 0, Lin2+ == 0
0 r0 = input;
1 r = r0 + r0;
2 return r;
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34. SUBJECTS USED
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Subject LoC # Versions Description
TCAS 135 41 Air Traffic Control
Schedule 304 9 Process scheduler
Schedule2 262 9 Process scheduler
Replace 518 29 Text processing
Grep 9366 2 Text search engine
SIR programs
Subject LoC
mknod 183
mkdir 159
mkfifo 107
cp 2272
GNU CoreUtils
Repaired by both GP and
SEMFIX.
Ours/GP = 0.63 (time)

35. WHY IS SEMFIX MORE STABLE?
0
5
10
15
20
25
30
35
40
45
10 20 30 40 50
Total
Semfix
GenProg
# tests
#ofprogramsrepaired
TCAS
Overall 90 programs from SIR
SemFix repaired 48/90, GenProg repaired 16/90 for 50 tests.
GenProg running time is >3 times of SemFix
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Time bound = 4 mins.
35

36. TYPE OF BUGS (SIR)
Total SemFix GenProg
Constant 14 10 3
Arithmetic 14 6 0
Comparison 16 12 5
Logic 10 10 3
Code
Missing
27 5 3
Redundant
Code
9 5 2
ALL 90 48 16
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37. EXAMPLE FIXES
 enabled = High_Confidence && (Own_Tracked_Alt_Rate <=
OLEV); /*&& (Cur_Vertical_Sep > MAXALTDIFF);missing
code*/
 Synthesizes missing code
 tmp = Up_Separation;
 Synthesizes
 tmp = ((OtherCapability < Alt_Layer_Value)?
 Two_of_Three_Reports_Valid:
 Cur_Vertical_Sep
 );
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38. STEPPING BACK, PERSPECTIVE
 [Obvious] Level of automation
 Never completely ~ Programming environments!
 Program synthesis likely to play a useful role.
 Is debugging required?
 Testing search and repair combined.
 Avoid statistical fault localization.
 Find the location to fix via symbolic reasoning and
MAXSAT – not clear about quality of repair produced.
 Can generate suggestions instead of repairs?
 What is a repair (or not) may depend on context.
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39. SPECIFIC APPLICATIONS OF REPAIR
 Role-based sanitization of HTML output
 XSS attacks – insert scripts into web-pages
 Role-based XSS sanitization – reduce false +ve
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WordPress, a popular blogging application, groups users into roles.
•A user in the author role can create a new post in the blog with
most non-code tags permitted.
•Anonymous commenter can use only few text formatting tags.
(S)he cannot insert images, but authors can.
•Neither can insert <script> tag or …
Un-trusted input flows into HTML tag context, but sanitizer applies
changes as function of the user role.
- Weinberger et al, ESORICS 2011.
Given the policy, a hand-in-hand test generation followed by (context-
sensitive) repair?

40. REFERENCES
 Path Exploration based on Symbolic Output Dawei Qi, Hoang D.T.
Nguyen, Abhik Roychoudhury, ESEC-FSE 2011, To appear in TOSEM.
 DARWIN: An Approach for Debugging Evolving Programs Dawei
Qi, Abhik Roychoudhury, Zhenkai Liang, Kapil Vaswani, ESEC-FSE
2009, TOSEM 21(3), 2012.
 SemFix: Program Repair via Semantic Analysis Hoang D.T.
Nguyen, Dawei Qi, Abhik Roychoudhury, Satish Chandra, ICSE 2013.
 Co-authors
 Dawei Qi, Zhenkai Liang, HDT Nguyen – NUS.
 Satish Chandra – IBM.
 Kapil Vaswani – MSR.
 Collaborator (ongoing)
 Prateek Saxena – NUS, Mattia Fazzini (visiting)
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