Generating minimal test set satisfying MC/DC criterion via SAT based approach

Abstract

The Modified Condition/Decision Coverage (MC/DC) is a test criterion proposed by NASA to measure the test set adequacy, especially in safety-critical systems. Existing works on test case generation for this criterion usually make use of greedy or meta-heuristic search techniques to construct a small test set. This paper studies the problem of generating optimal test set satisfying this criterion. It enumerates the size of test set from the theoretic lower-bound m + 1 to upper-bound 2m where m is the number of conditions that can be MC/DC covered, and then employs a SAT solver to decide whether there exists a test set with a given size, until a test set is found. We apply this method to benchmarks with no more than 25 conditions including dozens of instances collected from related works and millions of randomly generated ones. The experimental results indicate that most (more than 99%) of these instances can be MC/DC covered by a test set with only m + 1 test cases. Therefore, our SAT-based approach is efficient for generating optimal MC/DC test sets, since for most of the instances, it only invokes the SAT solver just once in the process of searching for minimal test set.