Analysis of a Hypertorus Grid

Abstract

Abstract structures of torus and hypertorus play a key role in nanotechnologies and are widely applied in nanotechnology for design of electronic devices and components. For modeling hypertorus structures, an infinite Petri net model has been developed and investigated. Based on the parametric specification of hypertorus models, an infinite system of linear homogenous equations has been derived. Using the earlier developed ad-hoc algorithm, a parametric solution of the system has been obtained. We can compose, in an explicit form, a solution that contains all the positive components. Thus, the model is a p-invariant Petri net for any given size and number of dimensions of hypertorus. Consequently, we can use storage elements of limited capacity for practical implementations of a hypertorus structure.