Minimal recurrence equation formulation of discrete event systems in max algebra

Abstract

In this paper, discrete event systems modelled by timed-event Petri nets are studied in the algebraic structure R/sub max/ that is an idempotent semifield. It is called max algebra or max-plus algebra in the literature. In this algebra, the equations describing evolution of the system have linear form and this allows the system to be analysed like systems in the conventional algebra. The application of the idea of an annulation polynomial or the idea of free vectors in the max algebra allow the authors to obtain a minimal recurrence equation of the system.