Um Sistema de Numeração Aplicado a Grafos a Eventos

Abstract

The objective of this paper is to show a numbering system directed to event graphs. To do so, we show two applications of this numbering system, the first one in arithmetic, to clarify the numbering system, and the other one in discrete event dynamic systems. This numbering system takes expressions from an alphabet. These expressions, also known as strings, are associated with integers. For each given alphabet, each expression can be put in unique correspondence with a positive integer. To illustrate this numbering system, the first application is in arithmetic. We show an arithmetic without the traditional zero symbols and compare it with the decimal numbering system used in elementary school. A different symbol is introduced, the square zero. One of the consequences of this system is that leading square zeros change the number being represented. The second application – the main objective in this paper – consists in using this numbering system to represent discrete event dynamic systems modeled by event graphs. As a consequence of this we hope that the properties of event graphs can be analyzed through the number theory since each expression, which determines a particular event graph, is associated to a single integer.