1. Dynamic Race Prediction in Linear Time
Dileep Kini
Umang Mathur
Mahesh Viswanathan
University of Illinois
at Urbana Champaign

2. Debugging concurrent programs is a nightmare
Reasoning about all possible inter-leavings !
Data Races, Deadlocks, ……
Fundamental Challenge !
Data Races

3. Data Races and How to Find Them
A data race occurs in an execution

4. Data Races and How to Find Them
A data race occurs in an execution when two concurrent threads consecutively accessing a shared memory location
Thread t1
Thread t2 1
acq(l) 2
r(x) 3
w(x) 4
rel(l)

5. Data Races and How to Find Them
A data race occurs in an execution when two concurrent threads consecutively accessing a shared memory location
At least one of the events is a write
Thread t1
Thread t2 1
acq(l) 2
r(x) 3
w(x) 4
rel(l)

6. Data Races and How to Find Them
A data race occurs in an execution when two concurrent threads consecutively accessing a shared memory location
At least one of the events is a write
Thread t1
Thread t2 1
acq(l) 2
r(x) 3
w(x) 4
rel(l)

7. Data Races and How to Find Them
Static Race Detection – Undecidable in general, false positives
Dynamic Race Detection
Lockset Based (Eraser) – false alarms
Sound Predictive Analysis
Happens Before (Lamport)
Causally Precedes (Smaragdakis et al)
Maximal Causal Models (Rosu et al)
Our technique detects more races and scales too !

8. Predictive Analysis
A given execution may not have a race, but can provide insights on other possible executions (by the same program) that exhibit race.
Thread t1
Thread t2 1
w(x) 2
acq(l) 3
r(x) 4
rel(l)
Thread t1
Thread t2 1
acq(l) 2
w(x) 3
r(x) 4
rel(l)
PREDICT
No data race

9. Predictive Analysis
A given execution may not have a race, but can provide insights on other possible executions (by the same program) that exhibit race.
Thread t1
Thread t2 1
w(x) 2
acq(l) 3
r(x) 4
rel(l)
Thread t1
Thread t2 1
acq(l) 2
w(x) 3
r(x) 4
rel(l)
PREDICT
No data race
Predictable data race
Data race uncovered

10. Predictive Analysis ❌ ❌
Any program that generates σ can also generate all its correct reorderings
Trace σ’ is a correct reordering of a trace σ if :
σ’|t is a prefix of σ|t for every thread t
Critical sections do not overlap
All reads in σ’ see the same values as in σ – last w(x) before any r(x) is the same in both σ and σ’
Thread t1
Thread t2 1
acq(l) 2
r(x) 3
rel(l) 4 5
w(x) 6
Thread t1
Thread t2 1
w(x) 2
acq(l) 3
r(x) 4
rel(l) 5 6 ❌ ❌

11. Predictive Analysis ❌ ❌
Trace σ’ is a correct reordering of a trace σ if :
σ’|t is a prefix of σ|t for every thread t
Critical sections do not overlap
All reads in σ’ see the same values as in σ – last w(x) before any r(x) is the same in both σ and σ’
Thread t1
Thread t2 1
acq(l) 2
r(x) 3
rel(l) 4 5
w(x) 6
Thread t1
Thread t2 1
w(x) 2
acq(l) 3
r(x) 4
rel(l) 5 6 ❌ ❌

12. Predictive Analysis Trace σ’ is a correct reordering of a trace σ if :
σ’|t is a prefix of σ|t for every thread t
Critical sections do not overlap
All reads in σ’ see the same values as in σ – last w(x) before any r(x) is the same in both σ and σ’
Predictive analysis techniques tend to check if there is a correct reordering of a given trace σ that exhibits a concurrency error, typically using partial orders over the events in σ

13. Predictive Analysis - HB
Thread t1
Thread t2 1
acq(l) 2
rel(l) 3 4
r(x) 5 6
w(x) 7
Pair of read/write events on same memory location performed by different threads, of which at least one is a write
Order events in a trace (≤HB ) :
Events inside a thread are ordered as seen in the trace.
Order critical sections as they appear in the trace.
Declare a race when two conflicting accesses are unordered.
Admits an online linear time algorithm 1 2
Data Race

14. Predictive Analysis - HB
Thread t1
Thread t2 1
acq(l) 2
r(x) 3
w(x) 4
rel(l) 5 6 7 8
Thread t1
Thread t2 1
w(y) 2
acq(l) 3
r(x) 4
rel(l) 5 6 7 8
r(y) 1 2 1 2
No HB race
No HB race
No predictable race

15. Predictive Analysis - HB
Thread t1
Thread t2 1
acq(l) 2
r(x) 3
w(x) 4
rel(l) 5 6 7 8
Thread t1
Thread t2 1
w(y) 2
acq(l) 3
r(x) 4
rel(l) 5 6 7 8
r(y)
No HB race
No HB race
No predictable race
Predictable race

16. Predictive Analysis - HB
Thread t1
Thread t2 1
acq(l) 2
r(x) 3
w(x) 4
rel(l) 5 6 7 8
Thread t1
Thread t2 1 2 3 4 5 6 7 8
HB is too conservative !
w(y)
acq(l)
r(x)
rel(l)
w(y)
acq(l)
r(x)
rel(l)
r(y)
No HB race
No HB race
No predictable race
Predictable race
r(y)

17. Predictive Analysis - CP†
<CP is the smallest transitive relation that orders e1 and e2 if:
e1 = rel(l), e2 = acq(l), and their critical sections have conflicting events
e1 = rel(l), e2 = acq(l), and their critical sections have events ordered by <CP.
∃e3 such that e1 ≤HB e3 <CP e2 or e1 <CP e3 ≤HB e2
Partial order ≤CP = <CP ∪Thread-order
Declare a race when two conflicting accesses are unordered.
acq(l)
r(x)
rel(l)
w(x) 1
acq(l) e
rel(l) e’ CP 2 e1 e3 e2 HB 3 CP
† Sound Predictive Race Detection in Polynomial Time, Y. Smaragdakis et al, POPL 2012

18. Predictive Analysis - CP
Thread t1
Thread t2 1
w(y) 2
acq(l) 3
w(x) 4
rel(l) 5 6
r(x) 7
r(y) 8
Thread t1
Thread t2 1
w(y) 2
acq(l) 3
w(x) 4
rel(l) 5 6
r(y) 7
r(x) 8 1
No CP race
No predictable race

19. Predictive Analysis - CP
Thread t1
Thread t2 1
w(y) 2
acq(l) 3
w(x) 4
rel(l) 5 6
r(x) 7
r(y) 8
Thread t1
Thread t2 1
w(y) 2
acq(l) 3
w(x) 4
rel(l) 5 6
r(y) 7
r(x) 8
No CP race
No predictable race

20. Predictive Analysis - CP
Thread t1
Thread t2 1
w(y) 2
acq(l) 3
w(x) 4
rel(l) 5 6
r(x) 7
r(y) 8
Thread t1
Thread t2 1
w(y) 2
acq(l) 3
w(x) 4
rel(l) 5 6
r(y) 7
r(x) 8 1
No CP race
No CP race
No predictable race

21. Predictive Analysis - CP
Thread t1
Thread t2 1
w(y) 2
acq(l) 3
w(x) 4
rel(l) 5 6
r(x) 7
r(y) 8
Thread t1
Thread t2 1 2 3 4 5 6 7 8
w(y)
w(y)
acq(l)
w(x)
rel(l)
r(y)
r(x)
w(y)
r(y)
acq(l)
r(y)
No CP race
No CP race
No predictable race
Predictable race missed by CP

22. Predictive Analysis - CP
CP misses races
CP does not have a linear time algorithm – fails to scale to traces having millions of events
Resort to windowing – can miss even HB races !
Remedy ?
Detects races missed by CP
WCP to the rescue
Linear running time

23. Weak Causal Precedence
<WCP is the smallest transitive relation that orders e1 and e2 if:
e1 = rel(l), e2 = r(x)/w(x) inside a critical section of lock l, and e2 conflicts with an event in crit. sec. of e1
e1 = rel(l), e2 = rel(l), and their critical sections have events ordered by <WCP
∃e3 such that e1 ≤HB e3 <WCP e2 or e1 <WCP e3 ≤HB e2
Partial order ≤WCP = <WCP ∪Thread-order
Declare a race when two conflicting accesses are unordered.
acq(l)
r(x)
rel(l)
w(x) 1
acq(l) e
rel(l) e’
WCP 2 e1 e3 e2 HB 3
WCP

24. WCP v/s CP
acq(l)
r(x)
rel(l)
w(x)
acq(l) e
rel(l) e’
WCP adds fewer orderings than CP, thus allowing for more correct re-orderings CP CP
WCP
WCP
Rule 1.
Rule 2.

25. WCP v/s CP 1 2 3 4 5 6 7 8 Thread t1 Thread t2 w(y) acq(l) w(x) rel(l)
r(y)
r(x)

26. WCP v/s CP 1 2 3 Predictable race caught by WCP
Thread t1
Thread t2 1 2 3 4 5 6 7 8
w(y)
acq(l)
w(x)
rel(l)
r(y)
r(x)
Predictable race missed by CP
Predictable race caught by WCP CP
WCP

27. WCP v/s CP 1 2 3 Predictable race caught by WCP
Thread t1
Thread t2 1 2 3 4 5 6 7 8
w(y)
w(y)
acq(l)
w(x)
rel(l)
r(y)
r(x)
Predictable race missed by CP
Predictable race caught by WCP
w(y)
r(y)
acq(l)
r(y)

28. Assumption - Nested locking paradigm
WCP Soundness
Assumption - Nested locking paradigm
WCP is weakly sound
Given any trace σ, if σ exhibits a WCP-race then σ exhibits a predictable race or a predictable deadlock
Any program generating σ can generate an execution σ’ (correct reordering) exhibiting a race/deadlock
Proof of soundness is non trivial. Soundness proof for CP was incorrect.
conflicting events unordered by ≤WCP

29. Vector Clock Algorithm
Assigns timestamp Ce to each event e, similar to HB vector clock algorithm
Timestamps are vector times (clocks) – thread indexed vectors, supporting various operations : comparison (⊑), join (⊔), update, etc.,
Ce ⊑ Ce’ iff e ≤WCP e’ – conflicting events with unordered timestamps imply a WCP race
One pass online algorithm – detects races as they occur
Processes events as they are generated, updates internal state (comprising of vector clocks and FIFO queues)

30. Vector Clock Algorithm
Linear running time – O(n) where n is the number of events
Worst case space requirement – O(n)
Empirically, the space overhead was observed to be small.
Optimal space usage – any single pass algorithm for WCP takes Ω(n) space
Optimal time/space tradeoff – For any algorithm computing WCP in time T(n) and space S(n), it must be the case that T(n)∙S(n) ∈Ω(n2)

31. Weak Causal Precedence
WCP detects all races (and deadlocks) detected by CP or HB, and even more
WCP admits a linear time algorithm
HB < CP < WCP
CP < HB ≈ WCP

32. Experimental Evaluation1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Program
LOC
#Events
#Thrds
#Locks
#Races
WCP Queue Length (%)
Time
WCP HB RV
Max
w=1K, s=60s
w=10K, s=240s
account 87
130
0.2s
0.3s 1s
airline 83
128
0.8s 2s
array 36 47
4.3
1.1s
boundedbuffer
334
333
bubblesort
274 4K
2.4
0.7s
0.5s
3.6s
7m3s
bufwriter
199
11.7M
47s
22.4s
4.1s
4.5s
critical 63 55
1.7s
0.9s
mergesort
298 3K
1.3
0.4s
1.4s
pingpong
124
146
1.2s
1.3s
moldyn
2.9K
164K 44
7.1s
2.4s
17.4s
montecarlo
7.2M
23.4s
16.2s
5.7s
raytracer
16K
14.7s
derby
302K
1.3M
1112 23 -
0.6 7s
31.2s TO
eclipse
560K
87M
8263 66 64
0.4
6m51s
4m18s
26.2s
15m10s
ftpserver
32K
49K
304
2.2
2.1s
3.8s 3m
jigsaw
101K 3M
280
18s
11.8s
2.8s
lusearch
410K
216M
118
160
10m13s
6m48s
57.3s
46.7s
xalan
180K
122M
2494 18
0.1
7m22s
4m46s
43.1s
7m11s

33. Experimental Evaluation1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Program
LOC
#Events
#Thrds
#Locks
#Races
WCP Queue Length (%)
Time
WCP HB RV
Max
w=1K, s=60s
w=10K, s=240s
account 87
130
0.2s
0.3s 1s
airline 83
128
0.8s 2s
array 36 47
4.3
1.1s
boundedbuffer
334
333
bubblesort
274 4K
2.4
0.7s
0.5s
3.6s
7m3s
bufwriter
199
11.7M
47s
22.4s
4.1s
4.5s
critical 63 55
1.7s
0.9s
mergesort
298 3K
1.3
0.4s
1.4s
pingpong
124
146
1.2s
1.3s
moldyn
2.9K
164K 44
7.1s
2.4s
17.4s
montecarlo
7.2M
23.4s
16.2s
5.7s
raytracer
16K
14.7s
derby
302K
1.3M
1112 23 -
0.6 7s
31.2s TO
eclipse
560K
87M
8263 66 64
0.4
6m51s
4m18s
26.2s
15m10s
ftpserver
32K
49K
304
2.2
2.1s
3.8s 3m
jigsaw
101K 3M
280
18s
11.8s
2.8s
lusearch
410K
216M
118
160
10m13s
6m48s
57.3s
46.7s
xalan
180K
122M
2494 18
0.1
7m22s
4m46s
43.1s
7m11s 6
WCP 4 2 8 3 7 44 5 23 66 36 14
160 18
Detects more races than other techniques

34. Experimental Evaluation1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Program
LOC
#Events
#Thrds
#Locks
#Races
WCP Queue Length (%)
Time
WCP HB RV
Max
w=1K, s=60s
w=10K, s=240s
account 87
130
0.2s
0.3s 1s
airline 83
128
0.8s 2s
array 36 47
4.3
1.1s
boundedbuffer
334
333
bubblesort
274 4K
2.4
0.7s
0.5s
3.6s
7m3s
bufwriter
199
11.7M
47s
22.4s
4.1s
4.5s
critical 63 55
1.7s
0.9s
mergesort
298 3K
1.3
0.4s
1.4s
pingpong
124
146
1.2s
1.3s
moldyn
2.9K
164K 44
7.1s
2.4s
17.4s
montecarlo
7.2M
23.4s
16.2s
5.7s
raytracer
16K
14.7s
derby
302K
1.3M
1112 23 -
0.6 7s
31.2s TO
eclipse
560K
87M
8263 66 64
0.4
6m51s
4m18s
26.2s
15m10s
ftpserver
32K
49K
304
2.2
2.1s
3.8s 3m
jigsaw
101K 3M
280
18s
11.8s
2.8s
lusearch
410K
216M
118
160
10m13s
6m48s
57.3s
46.7s
xalan
180K
122M
2494 18
0.1
7m22s
4m46s
43.1s
7m11s 12
WCP
0.2s
0.3s
0.7s
47s
0.4s
0.5s
7.1s
23.4s
2.4s
16.2s
6m51s
5.7s
18s
10m13s
7m22s
Fast

35. Experimental Evaluation1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Program
LOC
#Events
#Thrds
#Locks
#Races
WCP Queue Length (%)
Time
WCP HB RV
Max
w=1K, s=60s
w=10K, s=240s
account 87
130
0.2s
0.3s 1s
airline 83
128
0.8s 2s
array 36 47
4.3
1.1s
boundedbuffer
334
333
bubblesort
274 4K
2.4
0.7s
0.5s
3.6s
7m3s
bufwriter
199
11.7M
47s
22.4s
4.1s
4.5s
critical 63 55
1.7s
0.9s
mergesort
298 3K
1.3
0.4s
1.4s
pingpong
124
146
1.2s
1.3s
moldyn
2.9K
164K 44
7.1s
2.4s
17.4s
montecarlo
7.2M
23.4s
16.2s
5.7s
raytracer
16K
14.7s
derby
302K
1.3M
1112 23 -
0.6 7s
31.2s TO
eclipse
560K
87M
8263 66 64
0.4
6m51s
4m18s
26.2s
15m10s
ftpserver
32K
49K
304
2.2
2.1s
3.8s 3m
jigsaw
101K 3M
280
18s
11.8s
2.8s
lusearch
410K
216M
118
160
10m13s
6m48s
57.3s
46.7s
xalan
180K
122M
2494 18
0.1
7m22s
4m46s
43.1s
7m11s 3
#Events
130
128 47
333 4K
11.7M 55 3K
146
164K
7.2M
16K
1.3M
87M
49K 3M
216M
122M
Scales to large traces

36. Experimental Evaluation1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Program
LOC
#Events
#Thrds
#Locks
#Races
WCP Queue Length (%)
Time
WCP HB RV
Max
w=1K, s=60s
w=10K, s=240s
account 87
130
0.2s
0.3s 1s
airline 83
128
0.8s 2s
array 36 47
4.3
1.1s
boundedbuffer
334
333
bubblesort
274 4K
2.4
0.7s
0.5s
3.6s
7m3s
bufwriter
199
11.7M
47s
22.4s
4.1s
4.5s
critical 63 55
1.7s
0.9s
mergesort
298 3K
1.3
0.4s
1.4s
pingpong
124
146
1.2s
1.3s
moldyn
2.9K
164K 44
7.1s
2.4s
17.4s
montecarlo
7.2M
23.4s
16.2s
5.7s
raytracer
16K
14.7s
derby
302K
1.3M
1112 23 -
0.6 7s
31.2s TO
eclipse
560K
87M
8263 66 64
0.4
6m51s
4m18s
26.2s
15m10s
ftpserver
32K
49K
304
2.2
2.1s
3.8s 3m
jigsaw
101K 3M
280
18s
11.8s
2.8s
lusearch
410K
216M
118
160
10m13s
6m48s
57.3s
46.7s
xalan
180K
122M
2494 18
0.1
7m22s
4m46s
43.1s
7m11s 11
WCP Queue Length (%)
4.3
2.4 10
1.3
0.6
0.4
2.2
0.1
Low memory overhead

37. Conclusions WCP – generalizes the CP relation Linear time algorithm
Detects more races in practice
Scales to large traces
Future Work
Further weakening
Control flow information
Epoch based optimizations

38. Thank You !

40. WCP Deadlock Thread t1 Thread t2 Thread t3 1 acq(l) 2 acq(m) 3 rel(m)4
r(z) 5
rel(l) 6 7
acq(n) 8
sync(x) 9
rel(n) 10 11 12 13 14
w(z) 15 16
sync(y) 17 18

41. WCP Deadlock Thread t1 Thread t2 Thread t3 1 acq(l) 2 acq(m) 3 rel(m)4
r(z) 5
rel(l) 6 7
acq(n) 8
sync(x) 9
rel(n) 10 11 12 13 14
w(z) 15 16
sync(y) 17 18
acq(xlock)
r(xvar)
w(xvar)
rel(xlock)

42. WCP Deadlock Thread t1 Thread t2 Thread t3 WCP WCP 1 acq(l) 2 acq(m) 3
rel(m) 4
r(z) 5
rel(l) 6 7
acq(n) 8
sync(x) 9
rel(n) 10 11 12 13 14
w(z) 15 16
sync(y) 17 18
WCP
WCP

43. WCP race, but no predictable race
WCP Deadlock
Thread t1
Thread t2
Thread t3 1
acq(l) 2
acq(m) 3
rel(m) 4
r(z) 5
rel(l) 6 7
acq(n) 8
sync(x) 9
rel(n) 10 11 12 13 14
w(z) 15 16
sync(y) 17 18
WCP race, but no predictable race
WCP
WCP

44. WCP Deadlock Predictable deadlock Thread t1 Thread t2 Thread t3 acq(l)4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
acq(l)
acq(l)
acq(m)
rel(m)
r(z)
rel(l)
acq(n)
sync(x)
rel(n)
w(z)
sync(y)
acq(m)
Predictable deadlock
acq(m)
acq(n)
acq(n)
acq(l)