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User-Guided Program Reasoning using Bayesian Inference
Kihong Heo(joint work with Mukund Raghothaman, Sulekha Kulkarni, Mayur Naik)
University of Pennsylvania
Jul 6 2018 @ KAIST
�1
Conventional Static Analysis
Static AnalyzerSoundness
Precision Scalability
…
“needle in a haystack”
Designer User
!2
Why?
Static Analyzer
Designer User
!3
Soundness Precision Scalability
…
“needle in a haystack”
He does not know her: “What is the optimal strategy regarding
severity, context, idiom, etc?”
She does not know him: “Why does this alarm occur?”
“How to avoid the similar false alarms?”
“… can be difficult to do without introducing large numbers of false positives, or scaling performance exponentially poorly. In this case, balancing these and other factors in the analysis design caused us to miss the defect.”
— Coverity, On Detecting Heartbleed with Static Analysis, 2014
!4
Next-generation Static Analysis
Static Analyzer
!5
Next-generation Static Analysis
!6
Static Analyzer
Next-generation Static Analysis
!6
Static Analyzer
AI-based Analysis Design
• Human provides high-level idea
• AI provides detailed design choices
• DB accumulates performance data
• e.g.) precision [SAS’16,OOPSLA’17], soundness [ICSE’17], resource usage [in progress], rule learning [in progress]
Next-generation Static Analysis
!7
Static Analyzer
Next-generation Static Analysis
!7
Static Analyzer
AI-based Alarm Report
• AI prioritizes/classifies alarms
• Human inspects high confidence alarms
• DB accumulates human-labeled data
• e.g.) interactive alarm ranking [PLDI’18]
BINGO: An Interactive Alarm Ranking System
*User-Guided Program Reasoning using Bayesian Inference, PLDI’18
!8
Interactive Alarm Ranker
Bug
False Alarm
Rank 1
Rank n !9
Interactive Alarm Ranker
Bug
False Alarm
Rank 1
Rank n !10
Interactive Alarm Ranker
Bug
False Alarm
Rank 1
Rank n !11
Interactive Alarm Ranker
Bug
False Alarm
Rank 1
Rank n !12
Interactive Alarm RankerRank 1
Rank n !13
Key IdeaHuman in the loop + Bayesian inference
path(1,7)edge(7,2) edge(7,5)
path(1,2) path(1,5) edge(5,8)
path(1,8)edge(8,3) edge(8,6)
path(1,3) path(1,6)
edge(1,7)path(1,1)
f(){ v1 = new ...v2 = id1(v1)v3 = id2(v2)assert(v3!=v1) q1}id1(v){ return v }
g(){ v4 = new ...v5 = id1(v4)v6 = id2(v5)assert(v6!=v1) q2}id2(v){ return v }
Static Analysis Result Bayesian Network User
A B C ㄱCT T 0.95 0.05T F 0.94 0.06F T 0.29 0.71F F 0.01 0.99
B A ㄱA
T 0.52 0.48F 0.01 0.99
B ㄱB
0.04 0.96
A
C
B
!14
Case Study: Datarace
!15
Case Study: Information Flow
!16
Ex: Datarace Analysispublic class RequestHandler { private FtpRequest request;
public FtpRequest getRequest() { return request;
}
public void close() { synchronized (this) { if (isClosed) return; isClosed = true;
} controlSocket.close();controlSocket = null; request.clear();request = null;
} }
//L0
//L1 //L2 //L3
//L4 //L5 //L6 //L7
*Apache FTP Server
Parallel(p1, p3) :- Parallel(p1, p2), Next(p2, p3), Unguarded(p1, p3).Parallel(p1, p2) :- Parallel(p2, p1). Race(p1, p2) :- Parallel(p1, p2), Alias(p1, p2).
!17
Ex: Datarace Analysispublic class RequestHandler { private FtpRequest request;
public FtpRequest getRequest() { return request;
}
public void close() { synchronized (this) { if (isClosed) return; isClosed = true;
} controlSocket.close();controlSocket = null; request.clear();request = null;
} }
//L0
//L1 //L2 //L3
//L4 //L5 //L6 //L7
*Apache FTP Server
Datarace
Parallel(p1, p3) :- Parallel(p1, p2), Next(p2, p3), Unguarded(p1, p3).Parallel(p1, p2) :- Parallel(p2, p1). Race(p1, p2) :- Parallel(p1, p2), Alias(p1, p2).
!18
Ex: Datarace Analysispublic class RequestHandler { private FtpRequest request;
public FtpRequest getRequest() { return request;
}
public void close() { synchronized (this) { if (isClosed) return; isClosed = true;
} controlSocket.close();controlSocket = null; request.clear();request = null;
} }
//L0
//L1 //L2 //L3
//L4 //L5 //L6 //L7
*Apache FTP Server
False alarm
False alarm
Parallel(p1, p3) :- Parallel(p1, p2), Next(p2, p3), Unguarded(p1, p3).Parallel(p1, p2) :- Parallel(p2, p1). Race(p1, p2) :- Parallel(p1, p2), Alias(p1, p2).
!19
Derivation Graph
Parallel(p1, p3) :- Parallel(p1, p2), Next(p2, p3), Unguarded(p1, p3).Parallel(p1, p2) :- Parallel(p2, p1). Race(p1, p2) :- Parallel(p1, p2), Alias(p1, p2).
R(L6, L7)
A(L6, L7) P(L6, L7)
N(L6, L7) P(L6, L6)U(L6, L7)
N(L5, L6) P(L6, L5)U(L6, L6)
N(L4, L5) P(L6, L4)U(L6, L5)
P(L4, L6)
U(L4, L6)N(L5, L6)
R(L4, L5)
P(L4, L5)A(L4, L5)
U(L4, L5)N(L4, L5)P(L4, L4)controlSocket.close();controlSocket = null; request.clear();request = null;
//L4 //L5 //L6 //L7
Program
Datalog Rule
Derivation Graph
!20
Bayesian Network
P(L4,L4) N(L4,L5) U(L4,L5) Pr(P(L4,L5) | H)
TRUE TRUE TRUE 0.95
TRUE TRUE FALSE 0
…
FALSE FALSE FALSE 0
P(L4, L5)
Logical Rule Probabilistic Rule
Parallel(p1, p3) :- Parallel(p1, p2), Next(p2, p3), Unguarded(p1, p3).Parallel(p1, p2) :- Parallel(p2, p1). Race(p1, p2) :- Parallel(p1, p2), Alias(p1, p2).
U(L4, L5)N(L4, L5)P(L4, L4)
!21
*Prior probability is computed by an offline learning
Marginal Inference
R(L4, L5)
P(L4, L5)A(L4, L5)
Pr(R(L4,L5)) = Pr(R(L4,L5), A(L4,L5), P(L4,L5)) + Pr(R(L4,L5), ¬A(L4,L5), P(L4,L5)) + Pr(R(L4,L5), A(L4,L5), ¬P(L4,L5)) + Pr(R(L4,L5), ¬A(L4,L5), ¬P(L4,L5))
!22
U(L4, L5)N(L4, L5)P(L4, L4)
Marginal Inference
R(L4, L5)
P(L4, L5)A(L4, L5)
Pr(R(L4,L5)) = Pr(R(L4,L5), A(L4,L5), P(L4,L5)) + Pr(R(L4,L5), ¬A(L4,L5), P(L4,L5)) + Pr(R(L4,L5), A(L4,L5), ¬P(L4,L5)) + Pr(R(L4,L5), ¬A(L4,L5), ¬P(L4,L5))
If any of the antecedents fail, then the race cannot happen.
!23
U(L4, L5)N(L4, L5)P(L4, L4)
Marginal Inference
R(L4, L5)
P(L4, L5)A(L4, L5)
Pr(R(L4,L5)) = Pr(R(L4,L5), A(L4,L5), P(L4,L5))
!24
U(L4, L5)N(L4, L5)P(L4, L4)
Marginal Inference
R(L4, L5)
P(L4, L5)A(L4, L5)
Pr(R(L4,L5)) = Pr(R(L4,L5), A(L4,L5), P(L4,L5)) = Pr(R(L4,L5) | A(L4,L5), P(L4,L5)) * Pr(A(L4,L5)) * Pr(P(L4,L5))
By Bayes’s Rule: Pr(A,B) = Pr(A|B) * Pr(B)
!25
U(L4, L5)N(L4, L5)P(L4, L4)
Marginal Inference
R(L4, L5)
P(L4, L5)A(L4, L5)
Pr(R(L4,L5)) = Pr(R(L4,L5), A(L4,L5), P(L4,L5)) = Pr(R(L4,L5) | A(L4,L5), P(L4,L5)) * Pr(A(L4,L5)) * Pr(P(L4,L5)) = 0.95 * 1.0 * Pr(P(L4,L5)) = 0.95 * Pr(P(L4,L5), Pr(P(L4,L4)), Pr(N(L4,L5), Pr(U(L4,L5))
Assume that the probabilities of firing each rule and input tuple are
0.95 and 1.0.
!26
U(L4, L5)N(L4, L5)P(L4, L4)
Marginal Inference
R(L4, L5)
P(L4, L5)A(L4, L5)
Pr(R(L4,L5)) = Pr(R(L4,L5), A(L4,L5), P(L4,L5)) = Pr(R(L4,L5) | A(L4,L5), P(L4,L5)) * Pr(A(L4,L5)) * Pr(P(L4,L5)) = 0.95 * 1.0 * Pr(P(L4,L5)) = 0.95 * Pr(P(L4,L5), Pr(P(L4,L4)), Pr(N(L4,L5), Pr(U(L4,L5)) = 0.95 * Pr(P(L4,L5) | Pr(P(L4,L4)), Pr(N(L4,L5), Pr(U(L4,L5)) * Pr(P(L4,L4)) * Pr(N(L4,L5)) * Pr(U(L4,L5))
By Bayes’s Rule: Pr(A,B) = Pr(A|B) * Pr(B)
!27
U(L4, L5)N(L4, L5)P(L4, L4)
Marginal Inference
R(L4, L5)
P(L4, L5)A(L4, L5)
Pr(R(L4,L5)) = Pr(R(L4,L5), A(L4,L5), P(L4,L5)) = Pr(R(L4,L5) | A(L4,L5), P(L4,L5)) * Pr(A(L4,L5)) * Pr(P(L4,L5)) = 0.95 * 1.0 * Pr(P(L4,L5)) = 0.95 * 0.95 * Pr(P(L4,L4)) * Pr(N(L4,L5) * Pr(U(L4,L5)) = … = 0.398
!28
U(L4, L5)N(L4, L5)P(L4, L4)
Alarm Ranking
Ranking Alarm Confidence
1 R(L4, L5) 0.398
2 R(L5, L5) 0.378
3 R(L6, L7) 0.324
4 R(L7, L7) 0.308
5 R(L0, L7) 0.279
public class RequestHandler { private FtpRequest request;
public FtpRequest getRequest() { return request;
}
public void close() { synchronized (this) { if (isClosed) return; isClosed = true;
} controlSocket.close();controlSocket = null; request.clear();request = null;
} }
//L0
//L1 //L2 //L3
//L4 //L5 //L6 //L7
!29
Alarm Ranking
Ranking Alarm Confidence
1 R(L4, L5) 0.398
2 R(L5, L5) 0.378
3 R(L6, L7) 0.324
4 R(L7, L7) 0.308
5 R(L0, L7) 0.279
public class RequestHandler { private FtpRequest request;
public FtpRequest getRequest() { return request;
}
public void close() { synchronized (this) { if (isClosed) return; isClosed = true;
} controlSocket.close();controlSocket = null; request.clear();request = null;
} }
//L0
//L1 //L2 //L3
//L4 //L5 //L6 //L7
Q: What are the probabilities of the other alarms when R(L4,L5) is false?
!30
Marginal Inference
R(L6, L7)
A(L6, L7) P(L6, L7)
N(L6, L7) P(L6, L6)U(L6, L7)
N(L5, L6) P(L6, L5)U(L6, L6)
N(L4, L5) P(L6, L4)U(L6, L5)
P(L4, L6)
U(L4, L6)N(L5, L6)
R(L4, L5)
P(L4, L5)A(L4, L5)
U(L4, L5)N(L4, L5)P(L4, L4) Pr(P(L4,L5) | ¬R(L4,L5)) = Pr(¬R(L4,L5) | P(L4,L5)) * Pr(P(L4,L5)) / Pr(¬R(L4,L5))= 0.03
Pr(R(L6,L7) | ¬R(L4,L5)) = Pr(R(L6,L7) | P(L4,L5)) * Pr(P(L4,L5)) | ¬R(L4,L5))= 0.03
By Bayes’s Rule: Pr(A|B) = P(B|A) * Pr(A) / Pr(B)
!31
Alarm Ranking
Ranking Alarm Confidence
1 R(L4, L5) 0.398
2 R(L5, L5) 0.378
3 R(L6, L7) 0.324
4 R(L7, L7) 0.308
5 R(L0, L7) 0.279
Ranking Alarm Confidence
1 R(L0, L7) 0.279
2 R(L5, L5) 0.035
3 R(L6, L7) 0.030
4 R(L7, L7) 0.028
5 R(L4, L5) 0
!32
Experimental ResultsDatarace Analysis
0%
25%
50%
75%
100%
hedc ftp weblech jspider avrora luindex sunflow xalan
Bug Bingo Total!33
152 522 30 257 978 940 958 1870
Experimental ResultsDatarace Analysis
0%
25%
50%
75%
100%
hedc ftp weblech jspider avrora luindex sunflow xalan
Bug Bingo Total!34
152 522 30 257 978 940 958 1870Only 30% of alarms to discover all bugs
Experimental ResultsInformation Flow Analysis
0%
25%
50%
75%
100%
app-324 noisy app-ca7 app-kQm tilt andors ginger app-018
Bug Bingo Total!35
110 212 393 817 352 156 437 420
Experimental ResultsInformation Flow Analysis
0%
25%
50%
75%
100%
app-324 noisy app-ca7 app-kQm tilt andors ginger app-018
Bug Bingo Total!36
110 212 393 817 352 156 437 420Only 50% of alarms to discover all bugs
Future Work
!37
path(1,7)edge(7,2) edge(7,5)
path(1,2) path(1,5) edge(5,8)
path(1,8)edge(8,3) edge(8,6)
path(1,3) path(1,6)
edge(1,7)path(1,1)
f(){ v1 = new ...v2 = id1(v1)v3 = id2(v2)assert(v3!=v1) q1}id1(v){ return v }
g(){ v4 = new ...v5 = id1(v4)v6 = id2(v5)assert(v6!=v1) q2}id2(v){ return v }
A B C ㄱC
T T 0.95 0.05
T F 0.94 0.06
F T 0.29 0.71
F F 0.01 0.99
B A ㄱA
T 0.52 0.48
F 0.01 0.99
B ㄱB
0.04 0.96
A
C
B
1. Generalizing to non-datalog static analyses
2. Transferring the learned knowledge to other programs
3. Optimizing the marginal inference solver
4. Designing more fine-grained interaction models
1 23
4
Conclusion
• First interactive alarm ranking system
• Logical + probabilistic reasoning using Bayesian network
• Hope to build AI-guided static analysis system
!38
Conclusion
Thank You
!39
• First interactive alarm ranking system
• Logical + probabilistic reasoning using Bayesian network
• Hope to build AI-guided static analysis system
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