Reduction and Abstraction Techniques for Model Checking

Model checking is an increasingly popular method for verification of safety-critical systems. The main obstacle of this verification method is a state space explosion problem and consequently high computational requirements of model checking algorithms. In order to make the model checking method practically feasible, it is necessary to develop powerful techniques for fighting state space explosion. This thesis is focuses on fighting state space explosion in the context of embedded system verification. Verification of embedded systems is particularly difficult due to intricate interferences of software and real-time aspects of these systems. In this setting, the most useful techniques are abstraction and reduction. These represent the main topics of this thesis. The thesis contributes in several ways to the development of abstraction and reduction techniques, which are both practical and theoretically grounded. Our first contribution is the systematic presentation of reduction and abstraction techniques in a single formal setting. This facilitates understanding and application of these techniques. Our main innovative contribution lies in the novel under-approximation refinement algorithm for software model checking. Similarly to other automatic refinement algorithms, our algorithm is based on predicate abstraction. However, it uses under-approximation refinement instead of the classical over-approximation refinement. The thesis also contains several important technical results about abstraction and reduction techniques. Particularly, we provide two interesting results for timed automata: a decidability result for a non-emptiness problem of timed automata with sampled semantics and a new extrapolation technique for zone based abstractions of timed automata.