Verification of Square Lattices with Dedicated Channels by Infinite Petri Nets

Abstract structures of rectangular lattice with various edge conditions and neighborhoods play a key role in telecommunications, computing, nanotechnologies, and biological systems. For modeling rectangular structures, an infinite Petri net model has been developed and investigated. Based on the parametric specification of rectangular lattice models, an infinite system of linear homogenous equations has been derived. Using the earlier developed algorithm, a parametric solution of the system has been obtained, the solution contains all the positive components. Thus, the model is a p-invariant Petri net for any given size of square lattice. Consequently, we can use storage elements of limited capacity for practical implementations of a rectangular lattice structure.