Generic Semantics of Feature Diagrams

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Generic Semantics of Feature Diagrams

• Yves Bontemps
• Patrick Heymans
• Pierre-Yves Schobbens
• Jean-Christophe Trigaux
• Supported by First Europe project  Plenty 
  RWFSE
• ICFI 2005, Leicester

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Outline

• Introduction
• The Many Feature Diagrams
• Problems
• Solutions
• Varied Feature diagrams
• Tool support
• Complexity
• Conclusion Future Works

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Introduction

• Feature Modeling
• Identify commonality and variability
• Facilitates variant/configuration/version
  selection and management
• Feature Diagrams
• Describe allowed feature combinations
• Decision diagram
• Feature  A prominent and user-visible aspect,
  quality, or characteristic of a software system
  or systems. 

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The Many Feature Diagrams
Root

• FODA (OFD)

And-Node
XOr-Node
Optional Feature
Kang et al. 1990
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The Many Feature Diagrams

• FeatuRSEB

XOR
OR
Griss et al. 1998
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The Many Feature Diagrams

• Riebisch (EFD)

Variation point
Multiplicity

• Generative Programming Czarnecki
• Our VFD succinct, expressive, naturally embedded

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Problems

• What is the meaning of a FD?
• How to compare FD Notations?
• Is FDN1  more natural  than FDN2
• Is FDN1  more expressive  than FDN2
• Is FDN1  more succinct  than FDN2
• How to avoid redoing this work for each FD
  notation?
• Which FD Notation(FDN) to use?

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Solutions

• Our semantics of a FD
• The semantics of a FD is a Product Line
• The semantics of a Product Line is a set of
  products
• The semantics of a product is a set of features
• Here, features are formally left undefined

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Solutions

• Problem the meaning of a FD?
• a)
• b) F1,F2
• c) F1,F2,F3,F4
• d) F1,F2,F3,
  F1,F2,F4
• e)
• Solutions
• Language Syntax Semantics

F1
F2
F3
F4
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Generic Syntax

• A FD is a labeled graph with
• A set of Nodes N
• Nodes can bear a boolean operator
• Unique root,
• Can be leaves (F) i.e. effective features
• - Can be optional (O)
• Edges are acyclic, can be optional
• Constraints F are boolean formulae on N

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Syntax OFD

• Node types can be AND, XOR
• Constraints are binary, can be
• Requires (implication)
• Mutex ( not(A and B) )
• cannot be nested
• Nodes can be optional
• Edges cannot be optional

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Syntax EFD

• Node types can be AND, XOR, VP(i..j)
• Edges can be optional, nodes cannot
• Constraints are graphical, can be  Requires  or
   Mutex .

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Semantics

• Why Semantics?
• Make notation unambiguous
• Basis for correct tools
• Allows to state and solve questions of
  expressiveness, succinctness, etc.

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Semantics

• A model of a FD is a subset of its nodes s.t.
• The root is present in the model
• If a node is present, its sons satisfy its
  operator (type)
• The presence of a node must be justified by the
  presence one of its parents
• The constraints are satisfied
• Note constraints and links have different
  semantics

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Variant Edge-based semantics

• Riebisch hints at a semantics based on the
  inclusion of edges in a model

r
y
x
m
n
l
Is l,m a model of this diagram?
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Compare FD Notations

• Formal comparison criteria
• Expressiveness
• Embeddability
• Succinctness
• Redundancy

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Expressiveness

• Definition
• The expressiveness of L is E(L)
• E(L) D D ? L
• L1 is more expressive than L2 iff E(L2) ? E(L1)
• Results
• OFD is expressively complete
• Every product line can be described by an OFD
• No extension is more expressive than OFD !

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Embeddability

• Definition
• L1 is embeddable into L2 iff
• ? a translation T L1 ? L2 that is
• Correct T(D) D
• Node-controlled (compositional on graphs)
• Results
• OFD is embeddable into EFD

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Succintness

• Definition ( L1 G as succinct as L2)
• L2 ? G (L1) iff
• ? translation T L1 ? L2 that is
• Correct T(l1) l1
• Within G ? g ? G, ? n ? N, ? l1 ? L1, l1 ? n
  ? T(l1) ? g(n)
• Results
• EFD ? OFD
• VFD ? EFD, GPFD
• OFD ? O(EFD3)
• EFD can be cubically more succinct than OFD

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Redundancy

• Definition
• A language L is harmfully redundant iff L is (non
  trivially) self-embeddable
• A language L is harmlessly redundant iff
• ? D1 ¹ D2 ? L D1 D2
• Results
• OFD is not ambiguous but harmlessly redundant
• EFD is harmfully redundant

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Varied Feature Diagram (VFD)

• Definition
• VFD is a sublanguage of EFD with just VPs
• Results
• EFD is embeddable into VFD
• VFD is embeddable into EFD
• VFD ? 3.EFD
• VFD is not harmfully redundant

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Varied Feature Diagram (VFD)
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Tool Support

• Design FD
• Select product
• Compute systems/products
• Find Resolve conflicts
• Compare FD and present product(s) in the
  difference
• Compare FD described in different FD Notations

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Complexity

• Deciding wheter a FD has products is NP-complete
• Deciding wheter two FD are equivalent is
  coNP-complete. Giving a model in their difference
  is NP-complete.

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Conclusion

• Uniform Syntax Semantics of many FDN
• Evaluate/Compare FD Notations
• VFD is a succinct, natural and non-redundant
  language

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Future Work

• Variation points in other diagrams
• Features as transformations
• Evolution of product lines
• Late variability