In a Software Product Line (SPL), the central notion of implementability provides the requisite connection between specifications and their implementations, leading to the definition of products. While it appears to be a simple extension of the traceability relation between components and features, it involves several subtle issues that were overlooked in the existing literature. In this paper, we have introduced a precise and formal definition of implementability over a fairly expressive traceability relation. The consequent definition of products in the given SPL naturally entails a set of useful analysis problems that are either refinements of known problems or are completely novel. We also propose a new approach to solve these analysis problems by encoding them as Quantified Boolean Formulae (QBF) and solving them through Quantified Satisfiability (QSAT) solvers. QBF can represent more complex analysis operations, which cannot be represented by using propositional formulae. The methodology scales much better than the SAT-based solutions hinted in the literature and were demonstrated through a tool called SPLAnE (SPL Analysis Engine) on a large set of SPL models.
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