Abstract
This work presents some ideas and theory on representing ordinary Petri nets using matrices and builds on previous work in [11],[12]. The three main types of matrices used for Petri net representation are the input, output and incidence matrices. The motivation for this work is that matrices can provide an alternative way to describe Petri nets from the conventional graphical representation. As is indicated several properties can be inferred, observed and derived from the matrices. Some definitions and examples are used.
Highlights
Petri nets [1]-[4] are expressive graphical and mathematical formalisms that share a dual identity
The topographical structure of Petri nets is that these are composed of structured nodes and edges
The main reason for this paper it to explain the importance of Petri net representation using matrices
Summary
Petri nets [1]-[4] are expressive graphical and mathematical formalisms that share a dual identity These are useful for modelling concurrency in asynchronous, distributed, parallel, deterministic and other configurations. There is a lack of knowledge how to combine Petri nets with other formalisms and structures This is a possible challenge where to find a common basis. Boundedness, safeness, liveness, reversibility, home states, coverability, reachability are main properties that allow for simple verification These properties related to Petri net execution and structure are obtainable from the incidence matrix in conjunction with the marking vector and other values. Matrices are useful for representing the static structure of ordinary Petri nets. Matrices are useful to represent that part of Petri nets that does not require changes. The input flow, output flow matrices and the incidence matrix have special properties that can be used for different forms of analysis
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