Probability and Uncertainty in Software Engineering (keynote talk at NASAC 2013)

NASAC 2013,Tianjin, 9 November 2013
Probability and Uncertainty
in Software Engineering
David S. Rosenblum!
Dean, School of Computing!
National University of Singapore

Software Engineering 
at NUS
Hugh 
Anderson
Chin 
Wei Ngan
Dong 
Jin Song
Aquinas 
Hobor
Joxan!
Jaffar
Stan 
Jarzabek
Khoo 
Siau Cheng
Damith 
Rajapakse
David!
Rosenblum
Abhik 
Roychoudhury
Bimlesh 
Wadhwa
Yap 
Hock Chuan, 
Roland

Certainty in 
Software Engineering
Engineering of software is centered around
simplistic,“yes/no” characterizations of artifacts

Certainty in 
Engineering of software is centered around
simplistic,“yes/no” characterizations of artifacts
Program is correct/incorrect
Program execution finished/crashed
Compilation completed/aborted
Test suite succeeded/failed
Specification is satisfied/violated

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

Uncertainty in 
✓Nondeterminism
✓Randomized Algorithms
✓“Good Enough Software”
✓Test Coverage Metrics

Uncertainty in 
✓Nondeterminism
✓Randomized Algorithms
✓“Good Enough Software”
✓Test Coverage Metrics
Probabilistic Modeling and Analysis

Probabilistic 
Model Checking
! ¬p → ◊q( )∧"( )
Model
Checker
✓
✕
State Machine!
Model
Temporal 
Property
Results
Counterexample!
Trace
System
Requirements
P≥0.95 [ ]
0.4
0.6
Probabilistic
Probabilistic

Probabilistic 
Model Checking
! ¬p → ◊q( )∧"( )
Model
Checker
✓
✕
State Machine!
Model
Temporal 
Property
Results
Counterexample!
Trace
System
Requirements
P=? [ ]
0.4
0.6
Quantitative Results
0.9732Probabilistic
Probabilistic

Example 
Die Tossing Simulated by Coin Flipping
Knuth-Yao algorithm, 
from the PRISM group 
(Kwiatkowska et al.)
0
3
2
1
6
4
5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5

Example 
Die Tossing Simulated by Coin Flipping
Knuth-Yao algorithm, 
The behavior is governed by a!
theoretical probability distribution
0
3
2
1
6
4
5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5

Probabilistic 
Model Checking
! ¬p → ◊q( )∧"( )
Model
Checker
✓
State Machine!
Model
Temporal 
Property
Results
Counterexample!
Trace
System
Requirements
P≥0.95 [ ]
0.4
0.6
0.9732Probabilistic
Probabilistic

Probabilistic 
Model Checking
! ¬p → ◊q( )∧"( )
Model
Checker
✕
State Machine!
Model
Temporal 
Property
Results
Counterexample!
Trace
System
Requirements
P≥0.95 [ ]
Probabilistic
Probabilistic
0.41
0.59
0.6211

Example!
Zeroconf Protocol
s1s0 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

Example!
Zeroconf Protocol
s1s0 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
The behavior is governed by an!
empirically estimated probability distribution
packet-loss rate

Perturbed Probabilistic Systems!
(Current Research)
• Starting Points!
✓Discrete-Time Markov Chains (DTMCs)!
✓… with one or more probability parameters!
✓… veriﬁed against reachability properties:
S? ∪ S!
Guoxin Su and David S. Rosenblum, 
“Asymptotic Bounds for QuantitativeVeriﬁcation of Perturbed Probabilistic Systems”, 
Proc. ICFEM 2013

Parametric 
Markov Chains
• A distribution parameter in a DTMC is represented as a
vector x of parameters xi!
• The norm of total variance represents the amount of
perturbation:!
!
• The parameter is allowed a “sufﬁciently small”
perturbation with respect to ideal reference values r:!
!
• Can generalize to multiple parameters
v = vi∑
x − r ≤ Δ

Perturbation Bounds
• Perturbation Function!
!
where A is the transition probability sub-matrix for S?
and b is the vector of one-step probabilities from S? to S!
!
• Condition Numbers!
!
ρ x( )= ι? i A x
i
i b x( )− Ai
i b( )( )i=0
∞
∑
κ = lim
δ→0
sup
ρ(x − r)
δ
: x − r ≤ δ,δ > 0
⎧
⎨
⎩
⎫
⎬
⎭

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 —
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%

Additional Aspects
• Models
✓Markov Decision Processes (MDPs)!
✓Continuous-Time Markov Chains (CMTCs)
• Veriﬁcation
✓LTL Model Checking!
using Deterministic Rabin Automata!
✓PCTL Model Checking!
with singular perturbations due to nested P[ ] operators!
✓Reward Properties!
✓Alternative Norms and Bounds!
Kullback-Leibler Divergence, Quadratic Bounds

Other Forms 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

Uncertainty in Testing!
(New Research)
1982: Weyuker: Non-Testable Programs!
- Impossible/too costly to efﬁciently check results!
- Example: mathematical software!
2010: Garlan: Intrinsic Uncertainty!
- Systems embody intrinsic uncertainty/imprecision!
- Cannot easily distinguish bugs from “features”!
- Example: ubiquitous computing

Example!
Google Latitude
~ 500m
~ 50m
~ 2m

Example!
Google Latitude
When is an 
incorrect location!
a bug, and when 
is it a “feature”?
~ 500m
~ 50m
~ 2m

Example!
Google Latitude
When is an 
incorrect location!
a bug, and when 
is it a “feature”?
And how do!
you know?
~ 500m
~ 50m
~ 2m

Example!
Affective Computing

Example!
Affective Computing
When is an!
incorrect!
classiﬁcation a bug,!
and when is it a!
“feature”?

Example!
Affective Computing
When is an!
incorrect!
classiﬁcation a bug,!
and when is it a!
“feature”?
And how do!
you know?

Sources of 
Uncertainty
✓Output: results, characteristics of results!
✓Sensors: redundancy, reliability, resolution!
✓Context: sensing, inferring, fusing!
✓Machine learning: imprecision, user training

Sources of 
Uncertainty
✓Output: results, characteristics of results!
✓Sensors: redundancy, reliability, resolution!
✓Context: sensing, inferring, fusing!
✓Machine learning: imprecision, user training
These create signiﬁcant challenges for 
software engineering research and practice!

Conclusion
✓Software engineering (certainly) suffers
from excessive certainty!
✓A probabilistic mindset offers greater insight!
✓But signiﬁcant challenges remain for
probabilistic veriﬁcation!
✓And other forms of uncertainty are equally
challenging to address

Probability and Uncertainty
in Software Engineering
David S. Rosenblum!
Dean, School of Computing!
National University of Singapore
ThankYou!

Probability and Uncertainty in Software Engineering (keynote talk at NASAC 2013)

More Related Content

Similar to Probability and Uncertainty in Software Engineering (keynote talk at NASAC 2013)

More from David Rosenblum

Recently uploaded

Probability and Uncertainty in Software Engineering (keynote talk at NASAC 2013)