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Feature Diagrams & Logic There and Back Again
Krzysztof Czarnecki
University of Waterloo
Andrzej W ˛ asowski
IT University of Copenhagen
Feature Models
car
F eature D iagrams & L ogic T here and B ack A gain Krzysztof - - PowerPoint PPT Presentation
F eature D iagrams & L ogic T here and B ack A gain Krzysztof - - PowerPoint PPT Presentation
F eature D iagrams & L ogic T here and B ack A gain Krzysztof Czarnecki University of Waterloo Andrzej W asowski IT University of Copenhagen F eature M odels car F eature M odels car body engine gear keyless-entry power-locks F
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Feature Models
car power-locks keyless-entry gear engine body
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Feature Models
car power-locks keyless-entry gear engine body electric gas manual automatic
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Feature Models
car power-locks keyless-entry gear engine body electric gas manual automatic keyless-entry→power-locks
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Feature Models
car power-locks keyless-entry gear engine body electric gas manual automatic keyless-entry→power-locks
Model variability & commonality.
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Feature Models
car power-locks keyless-entry gear engine body electric gas manual automatic keyless-entry→power-locks
Model variability & commonality. Standard semantics:
φ(car, body, engine, gear, . . . )
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Semantics
car power-locks keyless-entry gear engine body electric gas manual automatic keyless-entry→power-locks
φ
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Reverse Engineering Syntax
?
φ
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Reverse Engineering Syntax
car power-locks keyless-entry gear engine body electric gas manual automatic keyless-entry→power-locks
φ
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Reverse Engineering Syntax
a → c a b c c a b a b c a, c b
φ
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Reverse Engineering Syntax
a b c
φ
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Contents
Motivation Syntax & Semantics (going there) Algorithm (going back again) Concluding remarks
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Contents
Motivation Syntax & Semantics (going there) Algorithm (going back again) Concluding remarks
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Theoretical Motivation
To deepen understanding of feature models To explore the relation between logics and FMs To characterize formulæ that are FMs without leftover constraint
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Applied Motivation
To visualize variability given as systems of constraints.
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Applied Motivation
To visualize variability given as systems of constraints. To guide the user interactively in visualizing constraints.
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Applied Motivation
To visualize variability given as systems of constraints. To guide the user interactively in visualizing constraints. To support refactoring tools.
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Applied Motivation
To visualize variability given as systems of constraints. To guide the user interactively in visualizing constraints. To support refactoring tools. To support reverse engineering FMs from code.
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Contents
Motivation Syntax & Semantics (going there) Algorithm (going back again) Concluding remarks
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Syntax: Going There
f
Solitary [1..1] → mandatory
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Syntax: Going There
f
Solitary [1..1] → mandatory
f
Solitary [0..1] → optional
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Syntax: Going There
f
Solitary [1..1] → mandatory
f
Solitary [0..1] → optional
f
Solitary [0..1] → grouped
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Syntax: Going There
f
Solitary [1..1] → mandatory
f
Solitary [0..1] → optional
f
Solitary [0..1] → grouped Group [1..1] → xor-group
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Syntax: Going There
f
Solitary [1..1] → mandatory
f
Solitary [0..1] → optional
f
Solitary [0..1] → grouped Group [1..1] → xor-group Group [1..k] → or-group
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Syntax: Going There
f
Solitary [1..1] → mandatory
f
Solitary [0..1] → optional
f
Solitary [0..1] → grouped Group [1..1] → xor-group Group [1..k] → or-group
φ
Left-over constraints
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Semantics: Going There
a b c d e f
a b c d e f
∧
a c ∨ e f
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Semantics: Going There
a b c d e f
a b c d e f
∧
a c ∨ e f
a b c d ∨ e f
An implication (hyper)graph
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Contents
Motivation Syntax & Semantics (going there) Algorithm (going back again) Concluding remarks
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Why Is It So Hard?
1. Possibly no models corresponding to φ
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Why Is It So Hard?
1. Possibly no models corresponding to φ 2. Possibly many models corresponding to φ
a → c a b c c a b a b c a, c b
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Why Is It So Hard?
1. Possibly no models corresponding to φ 2. Possibly many models corresponding to φ
a → c a b c c a b a b c a, c b
3. Brute-force infeasible
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Root Feature
Property The root of a feature tree Test A variable r implied by all the
- ther variables:
for all i. φ → (fi → r)
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Root Feature
Property The root of a feature tree Test A variable r implied by all the
- ther variables:
car power-locks keyless-entry gear engine body electric gas manual automatic keyless-entry→power-locks
body → car, gas → car, . . .
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Feature Hierarchy
Property
f is an ancestor of g (descendant)
Test Implication from descendant (g) to ancestor (f)
g → f
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Feature Hierarchy
Property
f is an ancestor of g (descendant)
Test Implication from descendant (g) to ancestor (f)
car power-locks keyless-entry gear engine body electric gas manual automatic keyless-entry→power-locks
body → car, gas → car, . . .
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Feature Hierarchy
Property
f is an ancestor of g (descendant)
Test Implication from descendant (g) to ancestor (f)
car power-locks keyless-entry gear engine body electric gas manual automatic keyless-entry→power-locks
Direct links: transitive reduction
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Mandatory Features
Property
g is a mandatory subfeature of f
Test Biimplication between variables corresponding to g and f
f → g
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Mandatory Features
Property
g is a mandatory subfeature of f
Test Biimplication between variables corresponding to g and f
car power-locks keyless-entry gear engine body electric gas manual automatic keyless-entry→power-locks
body → car, car → body, . . .
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And Groups
Property
g is a mandatory subfeature of f
Test Biimplication between variables corresponding to g and f
car power-locks keyless-entry gear engine body electric gas manual automatic keyless-entry→power-locks
And-groups: cliques in the graph
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Or Groups
Recall that for an or-group:
φ → (f → f1 ∨ · · · ∨ fk)
But then also
φ → (f → f1 ∨ · · · ∨ fk ∨ g)
holds for g other than fi.
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Or Groups
Implied disjunction can always be weakened! All implied disjunctions =
- versized and too-many or-groups
So detect minimal disjunctions
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Or Groups
Implied disjunction can always be weakened! All implied disjunctions =
- versized and too-many or-groups
So detect minimal disjunctions
{fi}i=1..k is a prime implicant of f
(see the paper) Prime implicants are well studied in fault tolerance analysis
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Or Groups
Property Or-groups of features rooted in f Test Find prime implicants of f
car power-locks keyless-entry gear engine body electric gas manual automatic keyless-entry→power-locks
electric ∧ gas → engine
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Or Groups
Property Or-groups of features rooted in f Test Find prime implicants of f
car power-locks keyless-entry gear engine body electric gas manual automatic keyless-entry→power-locks
manual ∧ electric ∧ gas → engine
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Algorithm
1 if unstatisfiable then quit 2 remove & report dead features 3 compute implication graph & its transitive reduction 4 find and-groups by contracting cliques 5 find all or-groups and xor-groups candidates
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Contents
Motivation Syntax & Semantics (going there) Algorithm (going back again) Concluding remarks
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Discussion (I)
Constructs an overapproximation (add a leftover constraint) The graph constructed contains maximum information (complete)
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Discussion (I)
Constructs an overapproximation (add a leftover constraint) The graph constructed contains maximum information (complete) Implemented using BDDs, algorithm by Coudert&Madre,1992 Efficient and scalable (computing prime implicants is the bottleneck)
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Discussion (II)
Semantic operations on feature models become logical operations
- n corresponding formulæ
Merge: (φFM1 → r) ∧ (φFM2 → r) Difference: φFM1 ∧ ¬φFM2 ...
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Future Work
Generalize the kind of models extracted beyond FODA Implement complex refactorings using logical representations Experiment with extracting models from code
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