Powerful Techniques for the

When proving invariance properties of programs one is faced with two problems. The rst problem is related to the necessity of proving tautologies of the considered assertion language, whereas the second manifests in the need of nding suuciently strong invariants. This paper focuses on the second problem and describes techniques for the automatic generation of invariants. The rst set of these techniques is applicable on sequential transition systems and allows to derive so-called local invari-ants, i.e. predicates which are invariant at some control location. The second is applicable on networks of transition systems and allows to combine local invariants of the sequential components to obtain local invariants of the global systems. Furthermore, a reened strengthening technique is presented that allows to avoid the problem of size-increase of the considered predicates which is the main drawback of the usual strengthening technique. The proposed techniques are illustrated by examples.