Synthesis of Attributed Feature Models From Product Descriptions

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

F2F0A1 A2

A2 < 8 => A1 >= 2A1 > 0 => A2 <= 2

Guillaume Bécan, Razieh Behjati, Arnaud Gotlieb, Mathieu Acher

Synthesis of Attributed Feature ModelsFrom Product Descriptions

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

Synthesis of Attributed Feature Models: Foundations 3

Product Lines/Highly configurable systems

config NR_CPUSint "Maximum number of CPUs" if SMP && !MAXSMPrange 2 8 if SMP && X86_32 && !X86_BIGSMPrange 2 512 if SMP && !MAXSMP && !CPUMASK_OFFSTACKrange 2 8192 if SMP && !MAXSMP && CPUMASK_OFFSTACK && X86_64default "1" if !SMPdefault "8192" if MAXSMPdefault "32" if SMP && X86_BIGSMPdefault "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

Synthesis of Attributed Feature Models: Foundations 4

● 2000+ options in about:config

● 3 types: boolean, integers, stringFirefox

Product Lines/Highly configurable systems

Synthesis of Attributed Feature Models: Foundations 5

Product Lines

Product comparison matrices

Comparison of digital SLRs

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

Synthesis of Attributed Feature Models: Foundations 7

From Configuration Matrix to AFM

#2 synthesis procedure#3 scalability evaluation

#1 semantics

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

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

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

F2F0A1 A2

root

F1

F3F2F0A1

A2

excludes

Synthesis

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

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 => F1F2 => A1 ∈ {0,2}¬ F2 => A1 ∈ {2,3}F2 => A2 ∈ {2,8}¬ F2 => A2 ∈ {0}…A1 = 2 => A2 ∈ {0,2}

Synthesis of Attributed Feature Models: Foundations 13

Synthesis algorithm● Define hierarchy (feature tree + place of attributes)

Binary implications...F2 => ¬ F1¬ F2 => F1F2 => 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

HierarchyPossible places for attributes¬ f => ( a = null value of a )

A1 : root, F0 A2 : root, F0, F2

A1 A2

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}

rootF1

F3F2 F0

Mutex graph

Solver

Binary implications

Possible feature groups

(Mutex, Or, Xor)

root

F1

F3

F2F0A1 A2+

+

Binary implication graph Hierarchy+ Mandatoryfeatures

Synthesis of Attributed Feature Models: Foundations 15

Synthesis algorithm● Compute readable constraints

Readable constraintsA1 > 0 => A2 <= 2A2 < 8 => A1 >= 2

Interesting valuesfor attributesA1 → 0A2 → 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}…

Mergeconstraints

Grammar of readable constraints

Synthesis of Attributed Feature Models: Foundations 16

User Effort

Domain knowledge =

● user input

● default heuristics

No user effortArbitrary choicesFully 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)

Synthesis of Attributed Feature Models: Foundations 17

ScalabilityRandom 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

Synthesis of Attributed Feature Models: Foundations 18

ScalabilityRandom 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 minMax: 62 min

Synthesis of Attributed Feature Models: Foundations 19

ScalabilityBest 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

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.

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)

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

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

F2F0A1 A2

A2 < 8 => A1 >= 2A1 > 0 => A2 <= 2

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/"

],...

}