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National University of Singapore
National University of Singapore
– Norman Vincent Peale, The Power of Posi,ve Thinking
“Do not build up obstacles in your imagina:on.”
Pop Quiz What Do These Things Have in Common?
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An Earthquake
Pop Quiz What Do These Things Have in Common?
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A Heart Attack
Pop Quiz What Do These Things Have in Common?
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President Trump
Pop Quiz What Do These Things Have in Common?
✓ They are governed by stochas:c phenomena
✓We have a reasonable understanding of their causes
✓We base our understanding on past observa:ons - At various levels of abstrac:on
(Simple) Answer: They are events to which
experts assign a probability based on models
Software is like this too!
Certainty inSoKware Engineering
“My program is correct.” “The specifica,on is sa,sfied.”
A simplistic viewpoint, which permeates most of our models, techniques and tools
Example Model Checking
! ¬p→◊q( )∧"( )
Model
Checker
✓✕
State Machine
Model
Temporal Property
Results
Counterexample
Trace
System
Requirements
Example Model Checking
! ¬p→◊q( )∧"( )
Model
Checker
✕
State Machine
Model
Temporal Property
Results
Counterexample
Trace
System
Requirements
Why Apply aProbabilis:c Viewpoint?
Why Apply aProbabilis:c Viewpoint?
Why Apply aProbabilis:c Viewpoint?
✓ Perfect and complete requirements are improbable
✓ Execu:on and tes:ng are akin to sampling … and we use tes:ng to increase confidence!
✓ The behavior of the execu:on environment is
random and unpredictable
✓ Frequency of execu:on failures is (hopefully) low
There are many random phenomena and “shades of grey”
in software engineering
But our models, techniques and tools rarely capture this
NATO Conference on SERome, 1969
h[p://homepages.cs.ncl.ac.uk/brian.randell/NATO/N1969/DIJKSTRA.html
– Edsger W. Dijkstra
(on more than one occasion!)
“Tes:ng shows the presence,
not the absence of bugs.”
Probabili:es at Garmisch, 1968 John Nash, IBM Hursley
h[p://homepages.cs.ncl.ac.uk/brian.randell/NATO/N1968/GROUP1.html
Naur & Randell, SoDware Engineering: Report on a Conference sponsored by the NATO Science CommiLee, Garmisch, Germany, 7th to 11th October 1968, January 1969.
Some Previous Efforts with
Probabilis:c Approaches• Performance Engineering (many)
• Cleanroom SoKware Engineering (Mills)
• Opera:onal Profiles and SoKware Reliability Engineering (Musa, …)
• Quan:ta:ve Goal Reasoning in KAOS (Lamsweerde, Le:er)
• Sta:s:cal Debugging (Harrold, Orso, Liblit, …)
• Probabilis:c Programming & Analysis (Poole, Pfeffer, Dwyer, Visser, …)
• Probabilis:c and Sta:s:cal Model Checking (many)
Probabilis:c Model Checking
! ¬p→◊q( )∧"( )
Model
Checker
✓✕
State Machine
Model
Temporal Property
Results
Counterexample
Trace
System
Requirements
P≥0.95 [ ]
0.4
0.6
Probabilis:c
Probabilis:c
Probabilis:c Model Checking
! ¬p→◊q( )∧"( )
Model
Checker
✓✕
State Machine
Model
Temporal Property
Results
Counterexample
Trace
System
Requirements
P=? [ ]
0.4
0.6
Quan:ta:ve Results
0.9732Probabilis:c
Probabilis:c
Example The Zeroconf Protocol
s1 s0 s2 s3
q
1
1
{ok} {error}
{start} s4
s5
s6
s7
s8
1
1-q
1-p
1-p
1-p 1-p
p p p
p
1
Pr(unsuccessful message probe)Pr(new address in use)
from the PRISM group(Kwiatkowska et al.)
P≤0.05 [ true U error ]
0.1 0.9
0.5
0.5
0.10.10.1
0.9
0.9
0.9
Some Previous Efforts with
Probabilis:c Approaches• Cleanroom SoKware Engineering
• Opera:onal Profiles & SoKware Reliability Engineering
• Quan:ta:ve Goal/Requirements Reasoning in KAOS
• Performance Engineering
• Sta:s:cal Debugging
• Probabilis:c Programming and Analysis
• Probabilis:c Model Checking
We lack an holistic approach
for the whole software development lifecycle
Challenges in Taking a
Probabilis:c Viewpoint
1. Some Things Are Certain, Or Should Be
2. Educa:on and Training
3. Popula:on Sizes and Sample Sizes
4. Determining the Probabili:es
5. Pinpoin:ng the Root Cause of Uncertainty
Challenges Some Things Are Certain, Or Should Be
Challenges Some Things Are Certain, Or Should Be
Challenges Some Things Are Certain, Or Should Be
Need to mix probabilistic and non-probabilistic approaches
Challenges Educa:on and Training
Challenges Educa:on and Training
Challenges Educa:on and Training
Challenges Educa:on and Training
Challenges Popula:on Sizes and Sample Sizes
Challenges Determining the Probabili:es
! ¬p→◊q( )∧"( )
Model
Checker
✓
State Machine
Model
Temporal Property
ResultsSystem
Requirements
P≥0.95 [ ]
0.4
0.6
Quan:ta:ve Results
0.9732Probabilis:c
Probabilis:c
Challenges Determining the Probabili:es
! ¬p→◊q( )∧"( )
Model
Checker
✕
State Machine
Model
Temporal Property
Results
Counterexample
Trace
System
Requirements
P≥0.95 [ ]
Quan:ta:ve Results
Probabilis:c
Probabilis:c
0.41
0.59
0.6211
Example The Zeroconf Protocol Revisited
s1 s0 s2 s3
q
1
1
{ok} {error}
{start} s4
s5
s6
s7
s8
1
1-q
1-p
1-p
1-p 1-p
p p p
p
1
from the PRISM group(Kwiatkowska et al.)
The packet-loss rate is determined by an
empirically es,mated probability distribu,on
Pr(packet loss)
0.1 0.9
0.5
0.5
0.10.10.1
0.9
0.9
0.9
Perturbed Probabilis:c Systems (Current Research)
• Discrete-Time Markov Chains (DTMCs) • “Small” perturba:ons of probability parameters
• Reachability proper:es P≤p[ ] • DRA proper:es
• Linear, quadra:c bounds on verifica:on impact
see papers at ICFEM 2013, ICSE 2014, CONCUR 2014,ATVA 2014, FASE 2016, ICSE 2016, IEEE TSE 2016
• Markov Decision Processes (MDPs)
• Con:nuous-Time Markov Chains (CTMCs)
S? U S!
Asympto:cPerturba:on Bounds
• Perturba:on Func:on
where A is the transi:on probability sub-matrix for S?
and b is the vector of one-step probabili:es from S? to S!
• Condi:on Number
• Predicted varia:on to probabilis:c verifica:onresult p due to perturba:on Δ:
ρ x( ) = ι? i A x i ib x( )− Ai ib( )( )i=0
∞
∑
κ = limδ→0
sup ρ(x − r)δ
: x − r ≤ δ ,δ > 0⎧⎨⎩
⎫⎬⎭
p̂ = p ±κΔ
Case Study Results Noisy Zeroconf (35000 Hosts, PRISM)
p Actual Collision Probability
Predicted Collision Probability
0.095 -19.8% -21.5%
0.096 -16.9% -17.2%
0.097 -12.3% -12.9%
0.098 -8.33% -8.61%
0.099 -4.23% -4.30%
0.100 1.8567 ✕ 10-4 —0.101 +4.38% +4.30%
0.102 +8.91% +8.61%
0.103 +13.6% +12.9%
0.104 +18.4% +17.2%
0.105 +23.4% +21.5%
Challenges Pinpoin:ng the Root Cause of Uncertainty
“There are known knowns; there are things we know we know. We also know
there are known unknowns; that is to say, we know there are some things we
do not know. But there are also unknown unknowns – the ones we don’t
know we don’t know.”
— Donald Rumsfeld
The Changing Nature ofSoKware Engineering
✓ Autonomous Vehicles
✓ Cyber Physical Systems
✓ Internet of Things
see
Deep Learning and Understandability versusSoDware Engineering and Verifica,on
by Peter Norvig, Director of Research at Google
h[p://www.youtube.com/watch?v=X769cyzBNVw
Example Affec:ve Compu:ng
Example Affec:ve Compu:ng
When is an incorrect emo,on
classifica,on a bug, and when is it a
“feature”?
And how do you know?
Uncertainty in Tes:ng (Current Research)
TestExecu:on
System
Under Test
Result Interpreta,on
Acceptable✓
Uncertainty in Tes:ng (Current Research)
TestExecu:on
System
Under Test
Result Interpreta,on
Unacceptable
Acceptable✓
✕
Uncertainty in Tes:ng (Current Research)
TestExecu:on
System
Under Test
Result Interpreta,on
Unacceptable
Acceptable
Acceptable
✓
✕
✕
Uncertainty in Tes:ng (Current Research)
TestExecu:on
System
Under Test
Result Interpreta,on
Unacceptable
Acceptable
Acceptable
✓
✕
✕
Acceptable misbehaviors can mask real faults!
One Possible Solu:on Distribu:on Fi{ng
System
Under Test
TrainingData WEKA
Sebastian Elbaum and David S. Rosenblum, “Known Unknowns: Testing in the Presence of Uncertainty”, Proc. FSE 2014.
One Possible Solu:on Distribu:on Fi{ng
System
Under Test
WEKA
Sebastian Elbaum and David S. Rosenblum, “Known Unknowns: Testing in the Presence of Uncertainty”, Proc. FSE 2014.
One Possible Solu:on Distribu:on Fi{ng
System
Under Test
Result Interpreta,on
Acceptablep < 0.99
TestExecu:on
WEKA
Sebastian Elbaum and David S. Rosenblum, “Known Unknowns: Testing in the Presence of Uncertainty”, Proc. FSE 2014.
One Possible Solu:on Distribu:on Fi{ng
System
Under Test
Result Interpreta,on
Unacceptable
Acceptablep < 0.99
TestExecu:on
WEKA
p < 0.0027
Sebastian Elbaum and David S. Rosenblum, “Known Unknowns: Testing in the Presence of Uncertainty”, Proc. FSE 2014.
One Possible Solu:on Distribu:on Fi{ng
System
Under Test
Result Interpreta,on
Unacceptable
Acceptable
Inconclusive
p < 0.99
TestExecu:on
WEKA
p < 0.37
p < 0.0027
Sebastian Elbaum and David S. Rosenblum, “Known Unknowns: Testing in the Presence of Uncertainty”, Proc. FSE 2014.
Conclusion
There is poten:ally much to be gained by relaxing the
tradi:onal absolu:st view of soKware engineering
And there are great research opportuni:es inapplying a probabilis:c viewpoint
– Norman Vincent Peale, The Power of Posi,ve Thinking
“Do not build up obstacles in your imagina:on.”
National University of Singapore
