On sequential modelling of non-sequential processes

Abstract

The aim of this paper is to answer the question whether all properties of discrete non-sequential processes can be expressed and proved in the framework of sequential descriptions of such processes. The paper deals only with the processes which can be defined in terms of Petri nets.

The rules according to which a process is running are represented by a Petri net. The process itself is identified with a Petri net of occurrences of conditions and events of this net. A characterization of these two nets, and of relationships between them, constitutes a theory of the process. Such a theory is objective in the sense of Petri.

A sequential description of a non-sequential process is a description of this process from the point of view of an external observer. The observer identifies the process with a sequence of occurrences of global states of the Petri net representing the rules of the process. A characterization of the last net, of the sequence of global net state occurrences, and of relationships between these two objects, is just a sequential description of the process, or a sequential theory of it. Such a theory is subjective in the sense of Petri.

The main result of the paper is that the objective theory of a process from a broad class of processes can be modelled in a subjective theory. It implies that the foundamental question of the paper may be answered positively for a class of processes.