Model checking

Abstract

In this chapter an introduction to model checking and model learning was given. Furthermore, it was shown how to combine both techniques to an approach in which properties of a SUT are verified directly. First of all we have presented Kripke transition systems which build a simple basis for temporal logics used in model checking. The essential difference between linear time logics and branching time logics was made plain on the basis of an example. Subsequently we presented linear time logic (LTL) and computational tree logic (CTL) which are widely used for model checking purposes. Since the combination of model checking and model learning for testing purposes is only meaningful with linear time logics we presented a basic model checking algorithm for linear time logic. In the second part of the chapter we first gave an introduction to the general ideas of model learning algorithms. Continuing in the same subject, we presented a number of learning algorithms; the observation pack algorithm, Angluin's algorithm, the reduced observation table algorithm and, the discrimination tree algorithm. Subsequently we discussed the algorithms' query complexity and presented some domain specific optimizations to reduce the number of queries. We rounded the model learning part off with some experimental results. The final part in this chapter presented the adaptive model checking algorithm, which combines model checking and model learning into one approach. The approach try to make use of information in an existing model of the SUT in order to save effort in the learning procedure. If no model exist or the existing model is irrelevant compared to the current SUT, the approach is still applicable. Although model checking and model learning are both established research areas, a lot of work remains to be done when considering testing. The combination of model checking and testing techniques should be clarified. Models to be used for testing might ask for different characteristics of the learning procedures than they currently have. For example, the construction of an abstract model of a SUT using learning algorithms might ask for a new approach. Issues in' this area need to be examined from a theoretical as well as practical point of view. © Springer-Verlag Berlin Heidelberg 2005.