Analysis of Extended Feature Models - In cooperation with Sven ...

Analysis of Extended Feature ModelsSebastian HennebergUniversity of PassauMarch 21, 2012In cooperation with Sven Apel, Don Batory and Thomas ThümSebastian Henneberg: Analysis of Extended Feature Models 1

MotivationIntroducing Attributes◮ feature attributes can represent quite different things:• cost, performance, binary size, requirements, compatibility, . . .Sebastian Henneberg: Analysis of Extended Feature Models 2

Motivation◮ automated support of feature model (FM) analysis has beendone using . . .• propositional logic based tools• constraint satisfaction problems• description logic◮ each approach examines just a few analysis operations⇒ No known work with Pseudo Boolean SAT Solvers tosupport FM analysis[Automated Analysis of Feature Models 20 Years LaterBenavides, Segura, Ruiz-Cortés in Information Systems, 2010]Sebastian Henneberg: Analysis of Extended Feature Models 3

SAT vs. PBSATSAT◮ input: conjunctive normal form (CNF)◮ output: has satisfiable variable assignment? [yes/no]◮ example: (x 1 ∨ ¬x 2 ∨ x 3 ) ∧ (x 2 ∨ ¬x 3 ∨ x 4 )PBSAT◮ input: linear (in)equations◮ output: has satisfiable variable assignment? [yes/no]◮ example: (3x 1 − 2x 2 + ¬x 3 = 2) ∧ (x 2 + ¬x 3 + x 4 ≥ 1)Sebastian Henneberg: Analysis of Extended Feature Models 4

SAT vs. PBSATSAT◮ input: conjunctive normal form (CNF)◮ output: has satisfiable variable assignment? [yes/no]◮ example: (x 1 ∨ ¬x 2 ∨ x 3 ) ∧ (x 2 ∨ ¬x 3 ∨ x 4 )PBSAT◮ input: linear (in)equations◮ output: has satisfiable variable assignment? [yes/no]◮ example: (3x 1 − 2x 2 + ¬x 3 = 2) ∧ (x 2 + ¬x 3 + x 4 ≥ 1)SAT boolean variable clause conjunction of clausesPBSAT 0-1 variable linear (in)equality conjunction of linear (in)equalitySebastian Henneberg: Analysis of Extended Feature Models 4

SAT vs. PBSATSAT◮ input: conjunctive normal form (CNF)◮ output: has satisfiable variable assignment? [yes/no]◮ example: (x 1 ∨ ¬x 2 ∨ x 3 ) ∧ (x 2 ∨ ¬x 3 ∨ x 4 )PBSAT◮ input: linear (in)equations◮ output: has satisfiable variable assignment? [yes/no]◮ example: (3x 1 − 2x 2 + ¬x 3 = 2) ∧ (x 2 + ¬x 3 + x 4 ≥ 1)SAT boolean variable clause conjunction of clausesPBSAT 0-1 variable linear (in)equality conjunction of linear (in)equalitySebastian Henneberg: Analysis of Extended Feature Models 4

Transformation of FMs to PBSAT◮ feature diagram and constraints are processed individually◮ transformation of feature diagram is straightforward◮ transformation of constraints is done after conversion to CNFr ≥ 1r − a ≥ 0r − b = 0b − c − d = 0−c + a ≥ 1Sebastian Henneberg: Analysis of Extended Feature Models 5

Transformation of FMs to PBSAT◮ feature diagram and constraints are processed individually◮ transformation of feature diagram is straightforward◮ transformation of constraints is done after conversion to CNFr ≥ 1r − a ≥ 0r − b = 0b − c − d = 0−c + a ≥ 1Sebastian Henneberg: Analysis of Extended Feature Models 5

Transformation of FMs to PBSAT◮ feature diagram and constraints are processed individually◮ transformation of feature diagram is straightforward◮ transformation of constraints is done after conversion to CNFr ≥ 1r − a ≥ 0r − b = 0b − c − d = 0−c + a ≥ 1Sebastian Henneberg: Analysis of Extended Feature Models 5

Transformation of FMs to PBSAT◮ feature diagram and constraints are processed individually◮ transformation of feature diagram is straightforward◮ transformation of constraints is done after conversion to CNFr ≥ 1r − a ≥ 0r − b = 0b − c − d = 0−c + a ≥ 1Sebastian Henneberg: Analysis of Extended Feature Models 5

Transformation of FMs to PBSAT◮ feature diagram and constraints are processed individually◮ transformation of feature diagram is straightforward◮ transformation of constraints is done after conversion to CNFr ≥ 1r − a ≥ 0r − b = 0b − c − d = 0−c + a ≥ 1Sebastian Henneberg: Analysis of Extended Feature Models 5

Transformation of FMs to PBSAT◮ feature diagram and constraints are processed individually◮ transformation of feature diagram is straightforward◮ transformation of constraints is done after conversion to CNFr ≥ 1r − a ≥ 0r − b = 0b − c − d = 0−c + a ≥ 1 (¬c ∨ a)Sebastian Henneberg: Analysis of Extended Feature Models 5

Transformation of FMs to PBSAT◮ feature diagram and constraints are processed individually◮ transformation of feature diagram is straightforward◮ transformation of constraints is done after conversion to CNFr ≥ 1r − a ≥ 0r − b = 0b − c − d = 0−c + a ≥ 1⇒ PBSAT can represent both basic and cardinality-based FMs!Sebastian Henneberg: Analysis of Extended Feature Models 5

Extending Feature ModelsPBSAT representation has integer coefficients⇒ What attribute types are possible?◮ single value integer• attribute = 3◮ integer ranges• attribute = [5,15]◮ finite integer sets• attribute = {3,5,7,9,11}◮ finite mutual exclusive choices (like enumerations)Sebastian Henneberg: Analysis of Extended Feature Models 6

Extending Feature ModelsPain of different interpretations◮ What are the semantics of range attributes? or integer sets?◮ IMHO: empty intersection leads to invalid product◮ interpretation not standardized yet / not enough input⇒ we focused on single value integer attributesSebastian Henneberg: Analysis of Extended Feature Models 7

Expressing Attributes and Constraintssample attributes file:Phone.cost = 25;GPS.cost = 30;Standard.cost = 20;HD.cost = 55;Camera.cost = 35;Sebastian Henneberg: Analysis of Extended Feature Models 8

Expressing Attributes and Constraintssample attributes file:sample constraints file:25 Phone + GPS.cost + Standard.cost +HD.cost + Camera.cost

Expressing Attributes and Constraintssample attributes file:sample constraints file:25 Phone + GPS.cost + Standard.cost +HD.cost + Camera.cost

Expressing Attributes and Constraintssample attributes file:sample constraints file:25 Phone + GPS.cost + Standard.cost +HD.cost + Camera.cost

Analysis OperationsDomain Engineering◮ Model Validation: Void◮ Feature Properties: Core, Variant, Dead, False Optional◮ Simplification: Atomic Sets◮ Edits: General., Special., Refactoring, ArbitrarySebastian Henneberg: Analysis of Extended Feature Models 9

Analysis OperationsDomain Engineering◮ Model Validation: Void◮ Feature Properties: Core, Variant, Dead, False Optional◮ Simplification: Atomic Sets◮ Edits: General., Special., Refactoring, ArbitrarySebastian Henneberg: Analysis of Extended Feature Models 9

Analysis OperationsDomain Engineering◮ Model Validation: Void◮ Feature Properties: Core, Variant, Dead, False Optional◮ Simplification: Atomic Sets◮ Edits: General., Special., Refactoring, ArbitrarySebastian Henneberg: Analysis of Extended Feature Models 9

Analysis OperationsDomain Engineering◮ Model Validation: Void◮ Feature Properties: Core, Variant, Dead, False Optional◮ Simplification: Atomic Sets◮ Edits: General., Special., Refactoring, ArbitrarySebastian Henneberg: Analysis of Extended Feature Models 9

Analysis OperationsDomain Engineering◮ Model Validation: Void◮ Feature Properties: Core, Variant, Dead, False Optional◮ Simplification: Atomic Sets◮ Edits: General., Special., Refactoring, ArbitrarySebastian Henneberg: Analysis of Extended Feature Models 9

Analysis OperationsApplication Engineering◮ Propagation of feature selectionsSebastian Henneberg: Analysis of Extended Feature Models 10

Work in progressComprehensive evaluation◮ random/generated feature models (Benavides, Thüm)◮ non-functional properties (Siegmund)◮ Kconfig models (Czarnecki, Berger)◮ non-software product lines (fast food, . . . )◮ extended feature models are rare in literature◮ companies do not provide models of their SPLs• . . . although they are configurable in webSebastian Henneberg: Analysis of Extended Feature Models 11

ContributionsPBSAT-related◮ PBSAT solvers for feature model analysis◮ transformation of feature models into PBSAT problems◮ PBSAT enables introduction of feature attributes◮ PBSAT can express additional constraints compact(even cardinality-based models!)◮ optimal products can be derived according to objective functionFeature Model Analysis◮ proposal of a new definition of variant features◮ proposal for new definition and computation of atomic setsSebastian Henneberg: Analysis of Extended Feature Models 12

Future Work◮ integration of further algorithms• redundancy detection• anomaly/problem resolutions• exaplanations• optimal products (based on objective function)◮ integration in FeatureIDE interface(current implementation is based on FeatureIDE models)◮ feasibility of other solvers or combinations of solversSebastian Henneberg: Analysis of Extended Feature Models 13

Future Work◮ integration of further algorithms• redundancy detection• anomaly/problem resolutions• exaplanations• optimal products (based on objective function)◮ integration in FeatureIDE interface(current implementation is based on FeatureIDE models)◮ feasibility of other solvers or combinations of solversWe are looking forward to receiving extended feature models!Sebastian Henneberg: Analysis of Extended Feature Models 13