Context. Variability-intensive programs (program families) appear in many application areas and for many reasons today. Different family members, called variants, are derived by switching statically configurable options (features) on and off, while reuse of the common code is maximized. Inquiry. Verification of program families is challenging since the number of variants is exponential in the number of features. Existing single-program analysis and verification tools cannot be applied directly to program families, and designing and implementing the corresponding variability-aware versions is tedious and laborious. Approach. In this work, we propose a range of variability-related transformations for translating program families into single programs by replacing compile-time variability with run-time variability (non-determinism). The obtained transformed programs can be subsequently analyzed using the conventional off-the-shelf singleprogram analysis tools such as type checkers, symbolic executors, model checkers, and static analyzers. Knowledge. Our variability-related transformations are outcome-preserving, which means that the relation between the outcomes in the transformed single program and the union of outcomes of all variants derived from the original program family is equality. Grounding. We present our transformation rules and their correctness with respect to a minimal core imperative language IMP. Then, we discuss our experience of implementing and using the transformations for efficient and effective analysis and verification of real-world C program families. Importance. We report some interesting variability-related bugs that we discovered using various state-of-theart single-program C verification tools, such as Frama-C, Clang, LLBMC. ACM CCS 2012Software and its engineering → Software creation and management Software verification and validation; Software notations and tools Formal language definitions;

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Abstract. Separate variability modeling adds variability to a modeling language without requiring modifications of the language or the supporting tools. We define a core language for separate variability modeling using a single kind of variation point to define transformations of software artifacts in object models. Our language, Featherweight VML, has several distinctive features. Its architecture and operations are inspired by the recently proposed Common Variability Language (CVL). Its semantics is considerably simpler than that of CVL, while remaining confluent (unlike CVL). We simplify complex hierarchical dependencies between variation points via copying and flattening. Thus, we reduce a model with intricate dependencies to a flat executable model transformation consisting of simple unconditional local variation points. The core semantics is extremely concise: it boils down to two operational rules, which makes it suitable to serve as a specification for implementations of trustworthy variant derivation. Featherweight VML offers insights in the execution of other variability modeling languages such as the Orthogonal Variability Model and Delta Modeling. To the best of our knowledge, this is the first attempt to comprehensively formalize variant derivation, encompassing feature models, variation points, implementation artifacts and transformations.

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