Spatial Specification of Grid Structures by Petri Nets

Abstract

To deal with models in grid computing (and systems biology as well), two basic ways of specifying spatial structures with Petri nets are considered—a colored Petri net and a parametric expression. We present a composition of hypertorus grid models in a form of parametric expression and colored Petri net, their mutual transformations, and unfolding into a place/transition net; the parameters are the number of dimensions and the size. The rules of mutual transformations of Petri net spatial specifications are studied. Colored Petri nets are convenient for the state space analysis. The main advantage of parametric expressions is the ability to obtain linear invariants and other structural constructs of Petri nets, for instance, siphons and traps, in parametric form that allows us to draw conclusions on Petri net properties for any values of parameters. Thus, we say that infinite grids (Petri nets) with definite spatial structure are investigated.