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