A Note on Generating Sets for Semiflows

TL;DR

This paper explores the properties of finite generating sets for semiflows in Petri Nets, analyzing their characteristics over various algebraic structures to uncover new theoretical insights.

Contribution

It introduces new results on generating sets for semiflows over semi rings and fields, enhancing understanding of their algebraic structure.

Findings

New characterizations of generating sets over semi rings and fields

Identification of conditions for finite generation of semiflows

Insights into the algebraic structure of semiflows in Petri Nets

Abstract

In this short note, we are interested in discussing characteristics of finite generating sets for $\mathcal{F}$, the set of all semiflows with non negative coefficients of a Petri Net. By systematically positioning these results over semi rings such as $\mathbb{N}$ or $\mathbb{Q^+}$ then over a field such as $\mathbb{Q}$, we were able to discover a handful of new results