Efficient fixpoint computation for invariant checking

Techniques for the computation of fixpoints are key to the success of many formal verification algorithms. To be efficient, these techniques must take into account how sets of states are represented. When BDDs are used, this means controlling, directly or indirectly, the size of the BDDs. Traditional fixpoint computations do little to keep BDD sizes small, apart from reordering variables. In this paper, we present a new strategy that attempts to keep the size of the BDDs under control at every stage of the computation. Our contribution includes also new techniques to compute partial images, and to speed up and test convergence. We present experimental results that prove the effectiveness of our strategy by demonstrating up to 40 orders of magnitude improvement in the number of states computed.