Symbolic Model Checking for Factored Probabilistic Models

The long line of research in probabilistic model checking has resulted in efficient symbolic verification engines. Nevertheless, scalability is still a key concern. In this paper we ask two questions. First, can we lift, to the probabilistic world, successful hardware verification techniques that exploit local variable dependencies in the analyzed model? And second, will those techniques lead to significant performance improvement on models with such structure, such as dynamic Bayesian networks? To the first question we give a positive answer by proposing a probabilistic model checking approach based on factored symbolic representation of the transition probability matrix of the analyzed model. Our experimental evaluation on several benchmarks designed to favour this approach answers the second question negatively. Intuitively, the reason is that the effect of techniques for reducing the size of BDD-based symbolic representations do not carry over to quantitative symbolic data structures. More precisely, the size of MTBDDs depends not only on the number of variables but also on the number of different terminals they have (which influences sharing), and which is not reduced by these techniques.