Avoiding Unreachable States

Abstract

The previous chapter has provided various examples of multidimensional MCs that are used to model systems composed of a finite number of interacting submodels. Assuming that there are H such interacting submodels, the state space of submodel h was denoted by $\mathcal{S}^{(h)}$ with $\mathcal{S}^{(h)} \subseteq \mathbb{Z}_{\geq 0}$ for h = 1, …, H, and $\mathcal{S} = \times _{h=1}^{H}\mathcal{S}^{(h)}$ represented the Cartesian product of the submodel state spaces. Because the Cartesian product of multiple submodel state spaces is used in its definition without any restriction on the state spaces themselves, $\mathcal{S}$ is called the H-dimensional product state space of the model.