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## Feature diagrams and logics: there and back again

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### Other Repositories/Bibliography

Venue: | in SPLC, 2007 |

Citations: | 69 - 4 self |

### Citations

3469 | Graph-based algorithms for boolean function manipulation
- Bryant
- 1986
(Show Context)
Citation Context ...n diagrams (BDDs). BDDs are widely used in hardware synthesis and model checking. Since our algorithm, presented later, relies on BDDs, we introduce them briefly here. For more information see, e.g., =-=[8, 3, 17]-=-. Any binary function can be represented using a binary decision tree (BDT). An example of BDT representing the binary function described by the formula (k → p)∧(p → c) is shown Figure 3. The formula ... |

925 |
Feature-oriented domain analysis (foda) feasibility study,” tech
- Kang, Cohen, et al.
- 1990
(Show Context)
Citation Context ...cations in reverse engineering and refactoring of feature models. 1 Introduction Feature modeling is a family of notations and an approach for modeling commonality and variability in product families =-=[15, 11, 4]-=-. In their basic form, feature models contain mandatory/optional features, feature groups, and implies and excludes relationships [12]. As shown by Batory [4], such feature models can be translated in... |

297 | Feature models, grammars, and propositional formulas
- Batory
- 2005
(Show Context)
Citation Context ...cations in reverse engineering and refactoring of feature models. 1 Introduction Feature modeling is a family of notations and an approach for modeling commonality and variability in product families =-=[15, 11, 4]-=-. In their basic form, feature models contain mandatory/optional features, feature groups, and implies and excludes relationships [12]. As shown by Batory [4], such feature models can be translated in... |

212 |
The transitive reduction of a directed graph
- Aho, Garey, et al.
(Show Context)
Citation Context ...tool can later decide to render such nodes as or-groups. All or-group nodes are tested whether they are not xor-groups and marked accordingly (25–26). Finally standard transitive reduction techniques =-=[1, 18]-=- are applied to the graph. The result is uniquely determined as our graph is acyclic at this point, after the cliques hadsbeen contracted. Even though visualizations of reduced graphs are much easier ... |

174 | Verification of synchronous sequential machines based on symbolic execution
- Coudert, Berthet, et al.
- 1989
(Show Context)
Citation Context ...ined automatically by simplifying ϕ with respect to a formula ψ resulting from translating the graph back to logics. One way to obtain this simplification is to use the algorithm for simplifying BDDs =-=[9, 3]-=-, translating them back to a propositional formula and using a generic formula simplifier. Consequently the interactive editor for feature models can use the computed graph to guide user safely, witho... |

170 | Automated Reasoning on Feature Models
- Benavides, Trinidad
- 2005
(Show Context)
Citation Context ...t feature configuration and feature model debugging. For example, Batory [4] explores the use of SAT solvers for that purpose. Van der Storm [20] considers BDD packages, and Benavides with colleagues =-=[6]-=- uses constraint solvers for the same purpose.sAll these consider the translation of feature models into logic and we are not aware of any work on extracting feature models from formulas. 9 Conclusion... |

166 | Synchronizing Cardinality-Based Feature Models and Their Specializations
- Kim, Czarnecki
- 2005
(Show Context)
Citation Context ...cations in reverse engineering and refactoring of feature models. 1 Introduction Feature modeling is a family of notations and an approach for modeling commonality and variability in product families =-=[15, 11, 4]-=-. In their basic form, feature models contain mandatory/optional features, feature groups, and implies and excludes relationships [12]. As shown by Batory [4], such feature models can be translated in... |

120 | Algorithms on Trees and Graphs - Valiente - 2001 |

80 | Implicit and incremental computation of primes and essential primes of Boolean functions
- Coudert, Madre
- 1992
(Show Context)
Citation Context ...at the resulting conjunction would not be an implicant of ϕ′. As prime implicants are widely used in reliability analysis and in hardware synthesis, several efficient methods for computing them exist =-=[10, 16]-=- and can be used in tools to identify or-groups. In order to see how finding prime implicants identifies or-groups, consider a slight transformation of formula (10): ϕ → (f → f1 ∨ · · · ∨ fk) ≡ ϕ → ( ... |

50 |
Refactoring product lines
- Alves, Gheyi, et al.
(Show Context)
Citation Context ...lf be useful as an internal representation of the problem in feature modeling and refactoring tools. Having such a graph at hand the tool can propose refactorings that go beyond the simple catalog of =-=[2]-=-.sQuality of the constructed graph The graph constructed by our algorithm is complete in the sense that it contains all and-group, or-group and xor-group candidates. It indicates all possible parent-c... |

46 | H.: Fast backtrack-free product configuration using a precompiled solution space representation
- Hadzic, Subbarayan, et al.
- 2004
(Show Context)
Citation Context ...esenting ϕ ∧ fi → fj for all pairs of variables in F , which would cost O(|F | 2 ·|ϕ|) time. Instead we construct BDDs representing ϕ ∧ fi for each of the linearly many fi’s and compute VALID-DOMAINS =-=[13, 14]-=- for variables in these BDDs. A valid domain for a variable f given a formula ϕ is the set of values that f can assume in satisfiable assignments of ϕ. Using the VALID-DOMAINS algorithm we can decide ... |

29 | Feature models are views on ontologies
- Czarnecki, Kim, et al.
- 2006
(Show Context)
Citation Context ...r modeling commonality and variability in product families [15, 11, 4]. In their basic form, feature models contain mandatory/optional features, feature groups, and implies and excludes relationships =-=[12]-=-. As shown by Batory [4], such feature models can be translated into propositional formulas. The translation enables the analysis and configuration using existing logic-based tools, such as SAT solver... |

27 | Variability and component composition
- Storm
- 2004
(Show Context)
Citation Context ... to the application of existing logic-based tools to support feature configuration and feature model debugging. For example, Batory [4] explores the use of SAT solvers for that purpose. Van der Storm =-=[20]-=- considers BDD packages, and Benavides with colleagues [6] uses constraint solvers for the same purpose.sAll these consider the translation of feature models into logic and we are not aware of any wor... |

26 |
A propositional logic-based method for verification of feature models
- Zhang, Zhao, et al.
- 2004
(Show Context)
Citation Context ...re replication. 8 Related work The relation between feature models and propositional logic has been studied by several authors, including Batory [4], Bontemps et al. [7], and Wei Zhang and colleagues =-=[21]-=-. The connection between feature models and logic has led to the application of existing logic-based tools to support feature configuration and feature model debugging. For example, Batory [4] explore... |

24 | Prime implicant computation using satisfiability algorithms
- Manquinho, Flores, et al.
- 1999
(Show Context)
Citation Context ...at the resulting conjunction would not be an implicant of ϕ′. As prime implicants are widely used in reliability analysis and in hardware synthesis, several efficient methods for computing them exist =-=[10, 16]-=- and can be used in tools to identify or-groups. In order to see how finding prime implicants identifies or-groups, consider a slight transformation of formula (10): ϕ → (f → f1 ∨ · · · ∨ fk) ≡ ϕ → ( ... |

13 |
A survey on the automated analyses of feature models
- Benavides, Ruiz-Cortés, et al.
- 2006
(Show Context)
Citation Context ...tablish its satisfiability, as otherwise it could create an ill-formed feature model that does not allow any configurations (not even the empty configuration). Dead features A given feature f is dead =-=[5]-=- if it is not present in any configurations of the feature diagram. Dead features are usually caused by modeling errors and should not be present in well formed feature models. Dead features have thei... |

5 |
Binary Decision Diagrams. Department of Information Technology
- Andersen
- 1997
(Show Context)
Citation Context ...n diagrams (BDDs). BDDs are widely used in hardware synthesis and model checking. Since our algorithm, presented later, relies on BDDs, we introduce them briefly here. For more information see, e.g., =-=[8, 3, 17]-=-. Any binary function can be represented using a binary decision tree (BDT). An example of BDT representing the binary function described by the formula (k → p)∧(p → c) is shown Figure 3. The formula ... |

5 |
Notes on calculating valid domains. Manuscript online http://www. itu.dk/~tarik/cvd/cvd.pdf
- Hadzic, Jensen, et al.
- 2006
(Show Context)
Citation Context ...esenting ϕ ∧ fi → fj for all pairs of variables in F , which would cost O(|F | 2 ·|ϕ|) time. Instead we construct BDDs representing ϕ ∧ fi for each of the linearly many fi’s and compute VALID-DOMAINS =-=[13, 14]-=- for variables in these BDDs. A valid domain for a variable f given a formula ϕ is the set of values that f can assume in satisfiable assignments of ϕ. Using the VALID-DOMAINS algorithm we can decide ... |

3 |
Generic semantics of feature diagrams variants
- Bontemps, Heymans, et al.
- 2005
(Show Context)
Citation Context ...the treatment of models with feature replication. 8 Related work The relation between feature models and propositional logic has been studied by several authors, including Batory [4], Bontemps et al. =-=[7]-=-, and Wei Zhang and colleagues [21]. The connection between feature models and logic has led to the application of existing logic-based tools to support feature configuration and feature model debuggi... |

1 |
Leeuwen. Maintanance of transitive closures and transitive reductions of graphs
- Poutré, van
- 1987
(Show Context)
Citation Context ...tool can later decide to render such nodes as or-groups. All or-group nodes are tested whether they are not xor-groups and marked accordingly (25–26). Finally standard transitive reduction techniques =-=[1, 18]-=- are applied to the graph. The result is uniquely determined as our graph is acyclic at this point, after the cliques hadsbeen contracted. Even though visualizations of reduced graphs are much easier ... |