Abstract. We present novel approaches to detect cardinality constraints expressed in CNF. The first approach is based on a syntactic analysis of specific data structures used in SAT solvers to represent binary and ternary clauses, whereas the second approach is based on a semantic analysis by unit propagation. The syntactic approach computes an approximation of the cardinality constraints AtMost-1 and AtMost-2 constraints very fast, whereas the semantic approach has the property to be generic, i.e. it can detect cardinality constraints AtMost-k for any k, at a higher computation cost. Our experimental results suggest that both approaches are efficient at recovering AtMost-1 and AtMost-2 cardinality constraints.
SUMMARYVariability determines the capability of software applications to be configured and customized. A common need during the development of variability-intensive systems is the automated analysis of their underlying variability models, e.g. detecting contradictory configuration options. The analysis operations that are performed on variability models are often very complex, which hinders the testing of the corresponding analysis tools and makes difficult, often infeasible, to determine the correctness of their outputs, i.e. the well-known oracle problem in software testing. In this article, we present a generic approach for the automated detection of faults in variability analysis tools overcoming the oracle problem. Our work enables the generation of random variability models together with the exact set of valid configurations represented by these models. These test data are generated from scratch using step-wise transformations and assuring that certain constraints (a.k.a. metamorphic relations) hold at each step. To show the feasibility and generalizability of our approach, it has been used to automatically test several analysis tools in three variability domains: feature models, CUDF documents and Boolean formulas. Among other results, we detected 19 real bugs in 7 out of the 15 tools under test.
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