Kronecker Based Matrix Representations for Large Markov Models

State-based analysis of discrete event systems notoriously suffers from the largeness of state spaces, which often grow exponentially with the size of the model. Since non-trivial models tend to be built by submodels in some hierarchical or compositional manner, one way to achieve a compact representation of the associated state-transition system is to use Kronecker representations that accommodate the structure of a model at the level of a state transition system. In this paper, we present the fundamental idea of Kronecker representation and discuss two different kinds of representations, namely modular representations and hierarchical representations. Additionally, we briefly outline how the different representations can be exploited in efficient analysis algorithms.