Verification of communication hexagonal grid with the infinite petri nets

A formal direct parametric description of the hexagonal grid model with side k is constructed according to the specified grid composition rules. A system of linear equations is constructed for finding invariants of positions on the basis of a direct description of the model. A method for calculating linear invariants of infinite Petri nets with a regular structure for an open hexagonal grid is used, and a solution of a system of linear equations in parametric form is obtained. It is proved that the hexagonal grid model, represented in the form of infinite Petri net, is a p-invariant Petri net for an arbitrary natural number k and has the boundedness and conservativeness properties. Communication grids, representing the implementation of the studied model, can be constructed using devices with limited capacity without overflow. ©2019 by Begell House, Inc.