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In the literature, the definition of product in a Software Product Line (SPL)is based upon the notion of consistency of the constraints, imposed byvariability and traceability relations on the elements of the SPL. In thispaper, we contend that consistency does not model the natural semantics of theimplementability relation between problem and solution spaces correctly.Therefore, we define when a feature can be {\em derived} from a set ofcomponents . Using this, we define a product of the SPL by a <specification,architecture> pair, where all the features in the specification are derivedfrom the components in the architecture. This notion of derivability isformulated in a simple yet expressive, abstract model of a productline withtraceability relation. We then define a set of SPL analysis problems and showthat these problems can be encoded as Quantified Boolean Formulas. Then, QSATsolvers like QUBE can be used to solve the analysis problems. We illustrate themethodology on a small fragment of a realistic productline.

Formalizing Traceability and Derivability in Software Product Lines