Pseudo-Boolean d-DNNF Compilation for Expressive Feature Modeling Constructs

Configurable systems typically consist of reusable assets that have dependencies between each other. To specify such dependencies, feature models are commonly used. As feature models in practice are often complex, automated reasoning is typically employed to analyze the dependencies. Here, the de facto standard is translating the feature model to conjunctive normal form (CNF) to enable employing off-the-shelf tools, such as SAT or #SAT solvers. However, modern feature-modeling dialects often contain constructs, such as cardinality constraints, that are ill-suited for conversion to CNF. This mismatch between the input of reasoning engines and the available feature-modeling dialects limits the applicability of the more expressive constructs. In this work, we shorten this gap between expressive constructs and scalable automated reasoning. Our contribution is twofold: First, we provide a pseudo-Boolean encoding for feature models, which facilitates smaller representations of commonly employed constructs compared to Boolean encoding. Second, we propose a novel method to compile pseudo-Boolean formulas to Boolean d-DNNF. With the compiled d-DNNFs, we can resort to a plethora of efficient analyses already used in feature modeling. Our empirical evaluation shows that our proposal substantially outperforms the state-of-the-art based on CNF inputs for expressive constructs. For every considered dataset representing different feature models and feature-modeling constructs, the feature models can be significantly faster translated to pseudo-Boolean than to CNF. Overall, deriving d-DNNFs from a feature model with the targeted expressive constraints can be substantially accelerated using our pseudo-Boolean approach. Furthermore, our approach is competitive on feature models with only basic constructs.

MulTi-Wise Sampling: Trading Uniform T-Wise Feature Interaction Coverage for Smaller Samples

Ensuring the functional safety of highly configurable systems often requires testing representative subsets of all possible configurations to reduce testing effort and save resources. The ratio of covered t-wise feature interactions (i.e., T-Wise Feature Interaction Coverage) is a common criterion for determining whether a subset of configurations is representative and capable of finding faults. Existing t-wise sampling algorithms uniformly cover t-wise feature interactions for all features, resulting in lengthy execution times and large sample sizes, particularly when large t-wise feature interactions are considered (i.e., high values of t). In this paper, we introduce a novel approach to t-wise feature interaction sampling, questioning the necessity of uniform coverage across all t-wise feature interactions, called \emph{\mulTiWise{}}. Our approach prioritizes between subsets of critical and non-critical features, considering higher t-values for subsets of critical features when generating a t-wise feature interaction sample. We evaluate our approach using subject systems from real-world applications, including \busybox{}, \soletta{}, \fiasco{}, and \uclibc{}. Our results show that sacrificing uniform t-wise feature interaction coverage between all features reduces the time needed to generate a sample and the resulting sample size. Hence, \mulTiWise{} Sampling offers an alternative to existing approaches if knowledge about feature criticality is available.