Tseitin or not Tseitin? The Impact of CNF Transformations on Feature-Model Analyses

Feature modeling is widely used to systematically model features of variant-rich software systems and their dependencies. By translating feature models into propositional formulas and analyzing them with solvers, a wide range of automated analyses across all phases of the software development process become possible. Most solvers only accept formulas in conjunctive normal form (CNF), so an additional transformation of feature models is often necessary. However, it is unclear whether this transformation has a noticeable impact on analyses. In this paper, we compare three transformations (i.e., distributive, Tseitin, and Plaisted-Greenbaum) for bringing featuremodel formulas into CNF. We analyze which transformation can be used to correctly perform feature-model analyses and evaluate three CNF transformation tools (i.e., FeatureIDE, KConfigReader, and Z3) on a corpus of 22 real-world feature models. Our empirical evaluation illustrates that some CNF transformations do not scale to complex feature models or even lead to wrong results for modelcounting analyses. Further, the choice of the CNF transformation can substantially influence the performance of subsequent analyses.

• Software and its engineering → Software configuration management and version control systems; • Theory of computation → Automated reasoning; • Computing methodologies → Representation of Boolean functions; • Hardware → Theorem proving and SAT solving.