1. root F0 F1 F2 F3 A1 A2
Yes Yes Yes No Yes 3 0
Yes Yes No Yes Yes 2 2
Yes Yes Yes No No 2 0
Yes Yes No Yes No 0 8
Synthesis
root
F1
F3
F2F0
A1 A2
A2 < 8 => A1 >= 2
A1 > 0 => A2 <= 2
Guillaume Bécan, Razieh Behjati, Arnaud Gotlieb, Mathieu Acher
Synthesis of Attributed Feature Models
From Product Descriptions

2. Notes
● Slides have been presented at SPLC'15
(Nashville, USA)
● Guillaume Bécan has made the vast
majority of the slides
● Some slides were previously presented at
FOSD'15 meeting
● Paper here:
https://hal.inria.fr/hal-01178454

3. Synthesis of Attributed Feature Models: Foundations 3
Product Lines/Highly configurable systems
config NR_CPUS
int "Maximum number of CPUs" if SMP && !MAXSMP
range 2 8 if SMP && X86_32 && !X86_BIGSMP
range 2 512 if SMP && !MAXSMP && !CPUMASK_OFFSTACK
range 2 8192 if SMP && !MAXSMP && CPUMASK_OFFSTACK && X86_64
default "1" if !SMP
default "8192" if MAXSMP
default "32" if SMP && X86_BIGSMP
default "8" if SMP
---help---
This allows you to specify the maximum number of CPUs which this
kernel will support. If CPUMASK_OFFSTACK is enabled, the maximum
supported value is 4096, otherwise the maximum value is 512. The
minimum value which makes sense is 2.
This is purely to save memory - each supported CPU adds
approximately eight kilobytes to the kernel image.
Linux kernel

4. Synthesis of Attributed Feature Models: Foundations 4
● 2000+ options in about:config
● 3 types: boolean, integers, string
Firefox
Product Lines/Highly configurable systems

5. Synthesis of Attributed Feature Models: Foundations 5
Product Lines
Product comparison matrices
Comparison of digital SLRs

6. Synthesis of Attributed Feature Models: Foundations 6
Modeling and Synthesis
● Boolean feature models (FMs) are nice but options are not only
boolean. Languages/operations have been defined on top of
attributed FMs; so where are attributed feature models?
● Numerous works address the synthesis of Boolean feature models,
eg [Czarnecki et al. SPLC'07, Andersen et al. SPLC'12, Davril et al.
FSE'13, Becan et al. ESE'15] but none of them consider attributes
●
We introduce for the first time an algorithmic and
parameterizable approach for synthesizing attributed
FMs from product descriptions

7. Synthesis of Attributed Feature Models: Foundations 7
From Configuration Matrix to AFM
#2 synthesis procedure
#3 scalability evaluation
#1
semantics

8. Synthesis of Attributed Feature Models: Foundations 8
Attributed Feature Model (AFM)
● AFM = attributed feature diagram + an arbitrary constraint
● Attributed feature diagram =
– Hierarchy of features
– Attributes: placed in features, they take a value in a domain
– Domain = set of values, null value and a partial order
– A set of human readable constraints

9. Synthesis of Attributed Feature Models: Foundations 9
Formalizing the AFM Synthesis Problem
● Configuration matrix = intermediate representation of a
set of configurations
● Given a configuration matrix, synthesize an AFM which is
– Maximal = the feature diagram contains as much as
possible information
– Sound and Complete = represent exactly the set of
configurations

10. Synthesis of Attributed Feature Models: Foundations 10
Formalizing the AFM Synthesis Problem
● Theoretical contributions (more details in the paper)
– Over-approximation of the attributed feature diagram
– Several AFMs are possible for one configuration matrix
root F0 F1 F2 F3 A1 A2
Yes Yes Yes No Yes 3 0
Yes Yes No Yes Yes 2 2
Yes Yes Yes No No 2 0
Yes Yes No Yes No 0 8
root
F1
F3
F2F0
A1 A2
root
F1
F3F2F0
A1
A2
excludes
Synthesis

11. Synthesis of Attributed Feature Models: Foundations 11
Synthesis algorithm
● Input: Configuration Matrix + Domain Knowledge ( )
● Output: AFM which is maximal, sound and complete
= user input + default heuristics
Tool name : FOReverSE

12. Synthesis of Attributed Feature Models: Foundations 12
Synthesis algorithm
● Extract feature, attributes and their domains
Features
● Root
● F0
● F1
● F2
● F3
Attributes
● A1 : {0,2,3}, 0
● A2 : {0,2,8}, 0
root F0 F1 F2 F3 A1 A2
Yes Yes Yes No Yes 3 0
Yes Yes No Yes Yes 2 2
Yes Yes Yes No No 2 0
Yes Yes No Yes No 0 8
● Compute binary implications
root F0 F1 F2 F3 A1 A2
Yes Yes Yes No Yes 3 0
Yes Yes No Yes Yes 2 2
Yes Yes Yes No No 2 0
Yes Yes No Yes No 0 8
...
F2 => ¬ F1
¬ F2 => F1
F2 => A1 ∈ {0,2}
¬ F2 => A1 ∈ {2,3}
F2 => A2 ∈ {2,8}
¬ F2 => A2 ∈ {0}
…
A1 = 2 => A2 ∈ {0,2}

13. Synthesis of Attributed Feature Models: Foundations 13
Synthesis algorithm
● Define hierarchy (feature tree + place of attributes)
Binary implications
...
F2 => ¬ F1
¬ F2 => F1
F2 => A1 ∈ {0,2}
¬ F2 => A1 ∈ {2,3}
F2 => A2 ∈ {2,8}
¬ F2 => A2 ∈ {0}
...
root
F1
F3
F2F0
Binary implication graph
(all possible hierarchies)
root
F1
F3
F2F0
Hierarchy
Possible places for attributes
¬ f => ( a = null value of a )
A1 : root, F0
A2 : root, F0, F2
A1 A2

14. Synthesis of Attributed Feature Models: Foundations 14
Synthesis algorithm
● Compute variability information (mandatory features, features groups)
– Only based on features
– Reuse existing algorithms (She et al., Inform Software Tech, 2014)
Xor: {F1, F2}
root
F1
F3
F2 F0
Mutex graph
Solver
Binary implications
Possible
feature groups
(Mutex, Or, Xor)
root
F1
F3
F2F0
A1 A2
+
+
Binary implication graph Hierarchy+ Mandatory
features

15. Synthesis of Attributed Feature Models: Foundations 15
Synthesis algorithm
● Compute readable constraints
Readable constraints
A1 > 0 => A2 <= 2
A2 < 8 => A1 >= 2
Interesting values
for attributes
A1 → 0
A2 → 8
Binary implications
...
A1 = 0 => A2 ∈ {8}
A1 = 2 => A2 ∈ {0,2}
A1 = 3 => A2 ∈ {0}
A2 = 0 => A1 ∈ {2,3}
A2 = 2 => A1 ∈ {2}
A2 = 8 => A1 ∈ {0}
…
Merge
constraints
Grammar of readable constraints

16. Synthesis of Attributed Feature Models: Foundations 16
User Effort
Domain knowledge =
● user input
● default heuristics
No user effort
Arbitrary choices
Fully automated algorithm
More user effort => better AFM
● Feature or attribute?
● Interpretation of the cells (“Yes”
= true)
● Hierarchy (F3 below F0)
● Overlapping feature groups
● Bounds in constraints (“0” is an
interesting value for A1)

17. Synthesis of Attributed Feature Models: Foundations 17
Scalability
Random dataset
● Generator of configuration matrices
– Number of variables (features + attributes)
– Number of configurations
– Maximum domain size (number of distinct values in a column)
● Execution time of or-group computation
● 1000 configurations
● max domain size of 10
Timeout always reached with
more than 60 variables
Or groups do not scale !
= default heuristics only

18. Synthesis of Attributed Feature Models: Foundations 18
Scalability
Random dataset
● Execution time (no or-groups)
● Up to 2,000 variables
● 1,000 configurations
● Max domain size of 10
● 100 variables
● Up to 200,000 configurations
● Max domain size of 10
● 10 variables
● 10,000 configurations
● Up to 6000 distinct values
= default heuristics only
On all experiments:
Average: 2.6 min
Max: 62 min

19. Synthesis of Attributed Feature Models: Foundations 19
Scalability
Best Buy dataset
Execution time of 2.1s for the most challenging matrix:
● 77 variables
● 185 configurations
● Maximum domain size of 185
Execution time is similar to the random dataset
● 242 matrices
● < 25% of empty cells
● Interpretation of empty cells = default heuristics only

20. Synthesis of Attributed Feature Models: Foundations 20
Conclusion
We introduce for the first time an algorithmic and
parameterizable approach for synthesizing attributed FMs
from product descriptions
Three key contributions:
● Semantics of attributed feature models/configuration
matrix (over- approximation, equivalence)
● We designed and implemented a tool-supported synthesis
algorithm
● We empirically evaluated the scalability of the synthesis
algorithm on random and real-world matrices.

21. Synthesis of Attributed Feature Models: Foundations 21
Future Work
● Empirical experiments provide evidence that the number
of constraints can be huge
– Random dataset: 237 constraints in average, 8906 max
– Best Buy dataset: 6821 constraints in average, 28300 max
● How to address the problem?
– Minimization, prioritization, user-specified
– Combination thereof
● Opencompare.org
– More empirical studies on realistic matrices (beyond Best
Buy)

22. Synthesis of Attributed Feature Models: Foundations 22
Future Work
● Take a set of constraints as input (rather
than a set of configurations)
– arbitrary propositional formula
– require the use of SMT/CP solvers
● Develop other operations on attributed
feature models: aggregate, merge, slice...
– Instance of synthesis problem

23. Synthesis of Attributed Feature Models: Foundations 23
Questions?
root F0 F1 F2 F3 A1 A2
Yes Yes Yes No Yes 3 0
Yes Yes No Yes Yes 2 2
Yes Yes Yes No No 2 0
Yes Yes No Yes No 0 8
Synthesis
root
F1
F3
F2F0
A1 A2
A2 < 8 => A1 >= 2
A1 > 0 => A2 <= 2

24. Synthesis of Attributed Feature Models: Foundations 24
Product Lines
{
"name": "Luke Skywalker",
"height": "1.72 m",
"mass": "77 Kg",
"hair_color": "Blond",
"skin_color": "Caucasian",
"eye_color": "Blue",
"birth_year": "19 BBY",
"gender": "Male",
"homeworld":
"http://swapi.co/api/planets/1/",
"films": [
"http://swapi.co/api/films/1/",
"http://swapi.co/api/films/2/",
"http://swapi.co/api/films/3/"
],
...
}
The Star Wars API (http://swapi.co/)
{
"name": "Darth Vader",
"height": "202",
"mass": "136",
"hair_color": "none",
"skin_color": "white",
"eye_color": "yellow",
"birth_year": "41.9BBY",
"gender": "male",
"homeworld":
"http://swapi.co/api/planets/1/",
"films": [
"http://swapi.co/api/films/6/",
"http://swapi.co/api/films/3/",
"http://swapi.co/api/films/2/",
"http://swapi.co/api/films/1/"
],
...
}