On homomorphisms of n-D behaviors

Different modeling procedures applied to a physical system may result in behaviors which are distinct but nevertheless share many structural properties. Such behaviors are isomorphic in a sense which we formalize and characterize in this paper. More generally, we introduce a natural notion of homomorphisms between behaviors of multidimensional systems, generalizing recent work of Fuhrmann. A generalization of strict system equivalence (in the sense of Fuhrmann) is shown to describe the relationship between generalized state-space descriptions in the nD case.