We show how the paradigm of learning-based testing (LBT) can be applied to automate specification-based black-box testing of reactive systems. Since reactive systems can be modeled as Kripke structures, we introduce an efficient incremental learning algorithm IKL for such structures. We show how an implementation of this algorithm combined with an efficient model checker such as NuSMV yields an effective learning-based testing architecture for automated test case generation (ATCG), execution and evaluation, starting from temporal logic requirements.