#### Formalizing Traceability and Derivability in Software Product Lines

##### Shankara Narayanan Krishna, Ganesh Narwane, Ramesh S., Swarup Mohalik, Jean-Vivien Millo

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

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