An algebraic structure of petri nets

Abstract

The paper concerns algebraic properties of Petrinets. A wide class of nets, called simple nets, is introduced and a lattice of these nets is defined. It turns out that nets representing sequential systems and processes are atoms of this lattice, and this fact provides the natural way of building nets representing. concurrent systems as the superposition of nets representing sequential system components. The notion of concurrency relation for large class of nets including cyclic nets is precisely defined. An influence of static, i.e. unmarked, structure of nets on the class of "proper" markings is discussed. The notion of natural markings, i.e. markings defined by the static (unmarked) structure of nets is introduced. Properties of safeness, compactness, fireability and K-density of marked nets are discussed. A classification of nets is proposed and an attempt of the algebraic definition of net with properties required from "well defined" dynamic concurrent system is given.