{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T08:50:13Z","timestamp":1782118213912,"version":"3.54.5"},"reference-count":43,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T00:00:00Z","timestamp":1776124800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002924","name":"Federaci\u00f3n Espa\u00f1ola de Enfermedades Raras","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002924","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005367","name":"Universidad Nacional de Educacion a Distancia","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100005367","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Spain Ministry of Science Innovation and Universities","doi-asserted-by":"publisher","award":["PID2022-138486OB-I00"],"award-info":[{"award-number":["PID2022-138486OB-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PID2022-142043NB-I00"],"award-info":[{"award-number":["PID2022-142043NB-I00"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011011","name":"Government of Andalusia","doi-asserted-by":"publisher","award":["PLSQ_00162"],"award-info":[{"award-number":["PLSQ_00162"]}],"id":[{"id":"10.13039\/501100011011","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["SoftwareX"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.softx.2026.102663","type":"journal-article","created":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T15:08:25Z","timestamp":1776438505000},"page":"102663","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Strong4VM: From variability models to strong transitive dependency and conflict graphs"],"prefix":"10.1016","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7131-0482","authenticated-orcid":false,"given":"Ruben","family":"Heradio","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luis","family":"Cambelo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miguel A.","family":"Olivero","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jose M.","family":"Sanchez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alberto","family":"Perez Garcia-Plaza","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Fernandez-Amoros","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.softx.2026.102663_bib0005","series-title":"Software product line engineering: foundations, principles and techniques","author":"Pohl","year":"2005"},{"key":"10.1016\/j.softx.2026.102663_bib0010","series-title":"SEI series in software engineering","article-title":"Software product lines: practices and patterns","author":"Clements","year":"2002"},{"key":"10.1016\/j.softx.2026.102663_bib0015","series-title":"Feature-Oriented software product lines: concepts and implementation","author":"Apel","year":"2013"},{"key":"10.1016\/j.softx.2026.102663_bib0020","series-title":"5th International workshop on variability modeling of Software-Intensive systems (VaMoS)","first-page":"119","article-title":"A comparison of decision modeling approaches in product lines","author":"Schmid","year":"2011"},{"key":"10.1016\/j.softx.2026.102663_bib0025","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1016\/j.jss.2018.12.027","article-title":"Software product lines and variability modeling: a tertiary study","volume":"149","author":"Raatikainen","year":"2019","journal-title":"J Syst Softw"},{"key":"10.1016\/j.softx.2026.102663_bib0030","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.scico.2012.06.002","article-title":"FeatureIDE: an extensible framework for feature-oriented software development","volume":"79","author":"Th\u00fcm","year":"2014","journal-title":"Sci Comput Program"},{"key":"10.1016\/j.softx.2026.102663_bib0035","series-title":"27th ACM international systems and software product line Conference (SPLC)","first-page":"16","article-title":"FLAMA: a collaborative effort to build a new framework for the automated analysis of feature models","volume":"vol. B","author":"Galindo","year":"2023"},{"issue":"6","key":"10.1016\/j.softx.2026.102663_bib0040","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1016\/j.is.2010.01.001","article-title":"Automated analysis of feature models 20 years later: a literature review","volume":"35","author":"Benavides","year":"2010","journal-title":"Inf Syst"},{"key":"10.1016\/j.softx.2026.102663_bib0045","series-title":"A formal study of free software distributions","author":"Boender","year":"2011"},{"key":"10.1016\/j.softx.2026.102663_bib0050","series-title":"International software product line Conference (SPLC)","first-page":"22","article-title":"Sample spaces and feature models: there and back again","author":"Czarnecki","year":"2008"},{"key":"10.1016\/j.softx.2026.102663_bib0055","series-title":"IEEE working Conference on software visualization (VISSOFT)","first-page":"50","article-title":"Feature relations graphs: a visualisation paradigm for feature constraints in software product lines","author":"Martinez","year":"2014"},{"key":"10.1016\/j.softx.2026.102663_bib0060","series-title":"International Systems and Software product line Conference (SPLC)","first-page":"309","article-title":"Using relation graphs for improved understanding of feature models in software product lines","author":"Duszynski","year":"2019"},{"key":"10.1016\/j.softx.2026.102663_bib0065","series-title":"40th International Conference on Software Engineering (ICSE)","first-page":"898","article-title":"Propagating configuration decisions with modal implication graphs","author":"Krieter","year":"2018"},{"key":"10.1016\/j.softx.2026.102663_bib0070","series-title":"Exploratory social network analysis with Pajek","author":"Nooy","year":"2018"},{"key":"10.1016\/j.softx.2026.102663_bib0075","series-title":"Statistical analysis of network data with r","author":"Kolaczyk","year":"2020"},{"key":"10.1016\/j.softx.2026.102663_bib0080","series-title":"Neo4j: the definitive guide: Hands-On recipes for production ready graph implementations","author":"Misquitta","year":"2025"},{"key":"10.1016\/j.softx.2026.102663_bib0085","series-title":"Network graph analysis and visualization with Gephi","author":"Cherven","year":"2013"},{"key":"10.1016\/j.softx.2026.102663_bib0090","doi-asserted-by":"crossref","DOI":"10.1016\/j.jss.2024.112326","article-title":"UVL: feature modelling with the universal variability language","volume":"225","author":"Benavides","year":"2025","journal-title":"J Syst Softw"},{"key":"10.1016\/j.softx.2026.102663_bib0095","article-title":"H","author":"Biere","year":"2021"},{"key":"10.1016\/j.softx.2026.102663_bib0100","series-title":"Differential testing for variational analyses: experience from developing KConfigReader","author":"K\u00e4stner","year":"2017"},{"key":"10.1016\/j.softx.2026.102663_bib0105","series-title":"23rd International Systems and Software Product line Conference (SPLC)","first-page":"303","article-title":"A kconfig translation to logic with one-way validation system","author":"Fernandez-Amoros","year":"2019"},{"key":"10.1016\/j.softx.2026.102663_bib0110","first-page":"15","article-title":"On computing backbones of propositional theories","volume":"215","author":"Marques-Silva","year":"2010","journal-title":"Frontiers in Artificial Intelligence and Applications"},{"issue":"2","key":"10.1016\/j.softx.2026.102663_bib0115","doi-asserted-by":"crossref","first-page":"161","DOI":"10.3233\/AIC-140640","article-title":"Algorithms for computing backbones of propositional formulae","volume":"28","author":"Janota","year":"2015","journal-title":"AI Commun"},{"key":"10.1016\/j.softx.2026.102663_bib0120","series-title":"International Conference on Theory and Applications of satisfiability testing (SAT)","first-page":"3:1","article-title":"CadiBack: extracting backbones with CaDiCaL","author":"Biere","year":"2023"},{"key":"10.1016\/j.softx.2026.102663_bib0125","series-title":"ACM international systems and software product line Conference (SPLC)","first-page":"54","article-title":"Collecting feature models from the literature: a comprehensive dataset for benchmarking","author":"Sundermann","year":"2024"},{"issue":"3","key":"10.1016\/j.softx.2026.102663_bib0130","doi-asserted-by":"crossref","DOI":"10.1145\/3764666","article-title":"How configurable is the linux kernel? Analyzing two decades of Feature-Model history\u2014RCR report","volume":"35","author":"Kuiter","year":"2026","journal-title":"ACM Trans Softw Eng Methodol"},{"key":"10.1016\/j.softx.2026.102663_bib0135","series-title":"IEEE\/ACM International Conference on automated software Engineering (ASE)","first-page":"1","article-title":"Scalable sampling of Highly-Configurable systems: generating random instances of the linux kernel","author":"Fernandez-Amoros","year":"2023"},{"key":"10.1016\/j.softx.2026.102663_bib0140","series-title":"The definitive ANTLR 4 reference","author":"Parr","year":"2013"},{"key":"10.1016\/j.softx.2026.102663_bib0145","series-title":"International Conference on Theory and Applications of satisfiability testing (SAT)","first-page":"502","article-title":"An extensible SAT-solver","author":"E\u00e9n","year":"2003"},{"key":"10.1016\/j.softx.2026.102663_bib0150","series-title":"36Th International Conference on Computer aided Verification (CAV)","first-page":"133","article-title":"CaDiCaL 2.0","author":"Biere","year":"2024"},{"key":"10.1016\/j.softx.2026.102663_bib0155","series-title":"Proc. Of SAT competition 2024\u2013solver, benchmark and proof checker descriptions","first-page":"8","article-title":"IsaSAT and kissat entering the SAT competition 2024","author":"Biere","year":"2024"},{"key":"10.1016\/j.softx.2026.102663_bib0160","series-title":"Accepted at International Conference on software and systems reuse, product lines, and configuration (VARIABILITY)","article-title":"Reasoning about variability models through network analysis","author":"Sanchez","year":"2026"},{"key":"10.1016\/j.softx.2026.102663_bib0165","series-title":"International software product line Conference (SPLC)","first-page":"7","article-title":"Feature models, grammars, and propositional formulas","author":"Batory","year":"2005"},{"key":"10.1016\/j.softx.2026.102663_bib0170","series-title":"27th ACM international systems and software product line Conference (SPLC)","first-page":"39","article-title":"UVLParser: extending UVL with language levels and conversion strategies","author":"Sundermann","year":"2023"},{"key":"10.1016\/j.softx.2026.102663_bib0175","series-title":"Logic in computer science: modelling and reasoning about systems","author":"Huth","year":"2004"},{"key":"10.1016\/j.softx.2026.102663_bib0180","series-title":"On the complexity of derivation in propositional calculus","first-page":"466","author":"Tseitin","year":"1983"},{"key":"10.1016\/j.softx.2026.102663_bib0185","series-title":"IEEE\/ACM International Conference on automated software Engineering (ASE)","first-page":"1","article-title":"Tseitin or not Tseitin? The impact of CNF transformations on Feature-Model analyses","author":"Kuiter","year":"2023"},{"key":"10.1016\/j.softx.2026.102663_bib0190","article-title":"Backbone computation for variability models: bridging the gap between the SAT and SPL communities","author":"Cambelo","year":"2026","journal-title":"arXiv preprint (under review at International Journal on Software and Systems Modeling)"},{"key":"10.1016\/j.softx.2026.102663_bib0195","series-title":"Exceptional c++: 47 engineering puzzles, programming problems, and solutions","author":"Herb","year":"1999"},{"key":"10.1016\/j.softx.2026.102663_bib0200","doi-asserted-by":"crossref","DOI":"10.1016\/j.jss.2024.112150","article-title":"UVLHub: a feature model data repository using UVL and open science principles","volume":"216","author":"Romero-Organvidez","year":"2024","journal-title":"J Syst Softw"},{"key":"10.1016\/j.softx.2026.102663_bib0205","doi-asserted-by":"crossref","DOI":"10.1016\/j.jss.2024.112235","article-title":"Leveraging belief uncertainty for informed decision making in software product line evolution","volume":"219","author":"Horcas","year":"2025","journal-title":"J Syst Softw"},{"key":"10.1016\/j.softx.2026.102663_bib0210","series-title":"Joint meeting on foundations of software engineering (ESEC\/FSE)","first-page":"291","article-title":"Is there a mismatch between real-world feature models and product-line research?","author":"Kn\u00fcppel","year":"2017"},{"key":"10.1016\/j.softx.2026.102663_bib0215","year":"2020"}],"container-title":["SoftwareX"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S2352711026001561?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S2352711026001561?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T08:19:54Z","timestamp":1782116394000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S2352711026001561"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":43,"alternative-id":["S2352711026001561"],"URL":"https:\/\/doi.org\/10.1016\/j.softx.2026.102663","relation":{},"ISSN":["2352-7110"],"issn-type":[{"value":"2352-7110","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Strong4VM: From variability models to strong transitive dependency and conflict graphs","name":"articletitle","label":"Article Title"},{"value":"SoftwareX","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.softx.2026.102663","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"102663"}}