Reverse engineering code dependencies: converting integer-based variability to propositional logic

A number of SAT-based analysis concepts and tools for software product lines exist, that extract code dependencies in propositional logic from the source code assets of the product line. On these extracted conditions, SAT-solvers are used to reason about the variability. However, in practice, a lot of software product lines use integer-based variability. The variability variables hold integer values, and integer operators are used in the conditions. Most existing analysis tools can not handle this kind of variability; they expect pure Boolean conditions. This paper introduces an approach to convert integer-based variability conditions to propositional logic. Running this approach as a preparation on an integer-based product line allows the existing SAT-based analyses to work without any modifications. The pure Boolean formulas, that our approach builds as a replacement for the integer-based conditions, are mostly equivalent to the original conditions with respect to satisfiability. Our approach was motivated by and implemented in the context of a real-world industrial case-study, where such a preparation was necessary to analyze the variability. Our contribution is an approach to convert conditions, that use integer variables, into propositional formulas, to enable easy usage of SAT-solvers on the result. It works well on restricted variables (i.e. variables with a small range of allowed values); unrestricted integer variables are handled less exact, but still retain useful variability information.