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 eature M odels car body engine gear keyless-entry power-locks electric gas manual automatic

F eature M odels keyless-entry → power-locks car body engine gear keyless-entry power-locks electric gas manual automatic

F eature M odels keyless-entry → power-locks car body engine gear keyless-entry power-locks electric gas manual automatic Model variability & commonality.

F eature M odels keyless-entry → power-locks car body engine gear keyless-entry power-locks electric gas manual automatic Model variability & commonality. Standard semantics: φ ( car , body , engine , gear , . . . )

S emantics keyless-entry → power-locks φ car body engine gear keyless-entry power-locks electric gas manual automatic

R everse E ngineering S yntax φ ?

R everse E ngineering S yntax keyless-entry → power-locks φ car body engine gear keyless-entry power-locks electric gas manual automatic

R everse E ngineering S yntax φ a c a a, c b c a b c b a → c b

R everse E ngineering S yntax φ a b c

C ontents Motivation Syntax & Semantics (going there) Algorithm (going back again) Concluding remarks

C ontents Motivation Syntax & Semantics (going there) Algorithm (going back again) Concluding remarks

T heoretical M otivation To deepen understanding of feature models To explore the relation between logics and FMs To characterize formulæ that are FMs without leftover constraint

A pplied M otivation To visualize variability given as systems of constraints.

A pplied M otivation To visualize variability given as systems of constraints. To guide the user interactively in visualizing constraints.

A pplied M otivation To visualize variability given as systems of constraints. To guide the user interactively in visualizing constraints. To support refactoring tools.

A pplied M otivation 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.

C ontents Motivation Syntax & Semantics (going there) Algorithm (going back again) Concluding remarks

S yntax: G oing T here f Solitary [1..1] → mandatory

S yntax: G oing T here f Solitary [1..1] → mandatory f Solitary [0..1] → optional

S yntax: G oing T here f Solitary [1..1] → mandatory f Solitary [0..1] → optional f Solitary [0..1] → grouped

S yntax: G oing T here f Solitary [1..1] → mandatory f Solitary [0..1] → optional f Solitary [0..1] → grouped Group [1..1] → xor-group

S yntax: G oing T here 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

S yntax: G oing T here 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

S emantics: G oing T here a a a b c d c ∧ b c d ∨ e f e f e f

S emantics: G oing T here a a a b c d c ∧ b c d ∨ e f e f e f a b c d ∨ e f An implication (hyper)graph

C ontents Motivation Syntax & Semantics (going there) Algorithm (going back again) Concluding remarks

W hy I s I t S o H ard? 1. Possibly no models corresponding to φ

W hy I s I t S o H ard? 1. Possibly no models corresponding to φ 2. Possibly many models corresponding to φ a c a a, c b c a b c b a → c b

W hy I s I t S o H ard? 1. Possibly no models corresponding to φ 2. Possibly many models corresponding to φ a c a a, c b c a b c b a → c b 3. Brute-force infeasible

R oot F eature P roperty The root of a feature tree T est A variable r implied by all the other variables: for all i . φ → ( f i → r )

R oot F eature P roperty The root of a feature tree T est A variable r implied by all the other variables: keyless-entry → power-locks car body engine gear keyless-entry power-locks electric gas manual automatic body → car , gas → car , . . .

F eature H ierarchy P roperty f is an ancestor of g (descendant) T est Implication from descendant ( g ) to ancestor ( f ) g → f

F eature H ierarchy P roperty f is an ancestor of g (descendant) T est Implication from descendant ( g ) to ancestor ( f ) keyless-entry → power-locks car body engine gear keyless-entry power-locks electric gas manual automatic body → car , gas → car , . . .

F eature H ierarchy P roperty f is an ancestor of g (descendant) T est Implication from descendant ( g ) to ancestor ( f ) keyless-entry → power-locks car body engine gear keyless-entry power-locks electric gas manual automatic Direct links: transitive reduction

M andatory F eatures P roperty g is a mandatory subfeature of f T est Biimplication between variables corresponding to g and f f → g

M andatory F eatures P roperty g is a mandatory subfeature of f T est Biimplication between variables corresponding to g and f keyless-entry → power-locks car body engine gear keyless-entry power-locks electric gas manual automatic body → car , car → body , . . .

A nd G roups P roperty g is a mandatory subfeature of f T est Biimplication between variables corresponding to g and f keyless-entry → power-locks car body engine gear keyless-entry power-locks electric gas manual automatic And-groups: cliques in the graph

O r G roups Recall that for an or-group: φ → ( f → f 1 ∨ · · · ∨ f k ) But then also φ → ( f → f 1 ∨ · · · ∨ f k ∨ g ) holds for g other than f i .

O r G roups Implied disjunction can always be weakened! All implied disjunctions = oversized and too-many or-groups So detect minimal disjunctions

O r G roups Implied disjunction can always be weakened! All implied disjunctions = oversized and too-many or-groups So detect minimal disjunctions { f i } i = 1.. k is a prime implicant of f (see the paper) Prime implicants are well studied in fault tolerance analysis

O r G roups P roperty Or-groups of features rooted in f T est Find prime implicants of f keyless-entry → power-locks car body engine gear keyless-entry power-locks electric gas manual automatic electric ∧ gas → engine

O r G roups P roperty Or-groups of features rooted in f T est Find prime implicants of f keyless-entry → power-locks car body engine gear keyless-entry power-locks electric gas manual automatic manual ∧ electric ∧ gas → engine

A lgorithm 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

C ontents Motivation Syntax & Semantics (going there) Algorithm (going back again) Concluding remarks

D iscussion (I) Constructs an overapproximation (add a leftover constraint) The graph constructed contains maximum information (complete)

D iscussion (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)

D iscussion (II) Semantic operations on feature models become logical operations on corresponding formulæ Merge: ( φ FM 1 → r ) ∧ ( φ FM 2 → r ) Difference: φ FM 1 ∧ ¬ φ FM 2 ...

F uture W ork Generalize the kind of models extracted beyond FODA Implement complex refactorings using logical representations Experiment with extracting models from code

S ummary Successful exercise in semantics Exhibited links between logical & relational phenomena and FMs implication graphs, transitive reduction, cliques, prime implicants Effective extraction procedure Implemented Suggested ideas for future work