Leopoldo Teixeira

Variability permeates software development to satisfy ever-changing requirements and mass-customization needs. A prime example is the Linux kernel, which employs the C preprocessor to specify a set of related but distinct kernel variants. To study, analyze, and verify variational software, several formal languages have been proposed. For example, the choice calculus has been successfully applied for type checking and symbolic execution of configurable software, while other formalisms have been used for variational model checking, change impact analysis, among other use cases. Yet, these languages have not been formally compared, hence, little is known about their relationships. Crucially, it is unclear to what extent one language subsumes another, how research results from one language can be applied to other languages, and which language is suitable for which purpose or domain. In this paper, we propose a formal framework to compare the expressive power of languages for static (i.e., compile-time) variability. By establishing a common semantic domain to capture a widely used intuition of explicit variability, we can formulate the basic, yet to date neglected, properties of soundness, completeness, and expressiveness for variability languages. We then prove the (un)soundness and (in)completeness of a range of existing languages, and relate their ability to express the same variational systems. We implement our framework as an extensible open source Agda library in which proofs act as correct compilers between languages or differencing algorithms. We find different levels of expressiveness as well as complete and incomplete languages w.r.t. our unified semantic domain, with the choice calculus being among the most expressive languages.

Configurable software systems offer user-selectable features to tailor them to the target hardware and user requirements. It is almost a rule that, as the number of features increases over time, unintended and inadvertent feature interactions arise. Despite numerous definitions of feature interactions and methods for detecting them, there is no procedure for determining whether the effect of a feature interaction could be, in principle, observed from an external perspective. In this paper, we devise a decision procedure to verify whether the effect of a given feature or potential feature interaction could be isolated by blackbox observations of a set of system configurations. For this purpose, we introduce the notion of blackbox observability, which is based on recent work on counterfactual reasoning on configuration decisions. Direct observability requires a single reference configuration to isolate the effect in question, while the broader notion of general observability relaxes this precondition and suffices with a set of reference configurations. We report on a series of experiments on community benchmarks as well as real-world configuration spaces and models. We found that (1) deciding observability is indeed tractable in real-world settings, (2) constraints in real-world configuration spaces frequently limit observability, and (3) blackbox performance models often include effects that are de facto not observable.