Infinite behavior of continuous and discrete nets

In this paper, we present an equational representation of the dynamic of weighted discrete and continuous Petri nets. Under canonical form, these equations can be written as a coupling between a linear system, in the (min,+) algebra and a linear equation in the classical sense. We derive an algorithm to check liveness of weighted routed nets based on the total number of event equations for each single input subnet and on a continuous approximation of a Petri net that provides linear equation descriptions. Structural properties such as liveness are reduced to linear algebra notions such as spectral radius of matrices or existence of non-negative solutions in linear equations.