The Benefits of Sometimes Not Being Discrete

Discrete representations of systems are usual in theoretical computer science and they have many benefits. Unfortunately they also suffer from the problem of state space explosion, sometimes termed the curse of dimensionality. In recent years, research has shown that there are cases in which we can reap the benefits of discrete representation during system description but then gain from more efficient analysis by approximating the discrete system by a continuous one. This paper will motivate this approach, explaining the theoretical foundations and their practical benefits.