The max-plus algebra is one of the frameworks that can be used to model discrete event systems. One of the open problems in the max-plus-algebraic system theory for discrete event systems is the minimal realization problem. In this paper we present some results for a simplified version of the general minimal realization problem: the boolean minimal realization problem, i.e., we consider models ...

In this overview report we present known results and open problems in connection with the minimal state space realization problem in the max-plus algebra, which is a framework that can be used to model a class of discrete event systems. 1 Description of the problem Given an n×n matrix A, an n×1 vector b and a 1×n vector c one can construct the sequence gi, i = 1, 2, . . ., where gi is defined b...

In this paper we show that finding solutions of a system of multivariate polynomial equalities and inequalities in the max algebra is equivalent to solving an Extended Linear Complementarity Problem. This allows us to find all solutions of such a system of multivariate polynomial equalities and inequalities and provides a geometrical insight in the structure of the solution set. We also demonst...

We present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCK-algebra induced by a max-min general fuzzy automaton. Then, we study the properties of this hyper BCK-algebra. Particularly, some theorems and results for hyper BCK-algebra are proved. For example, it is shown that this structure consists of different ty...

The minimal realization problem in the max-plus algebra, " Chapter 32 in Open Problems in Mathematical Systems and Control Theory

A square array whose all rows and columns are different permutations of the same length over symbol set is known as a Latin square. may or not be symmetric. For classification enumeration purposes, symmetric, non-symmetric, conjugate totally symmetric squares play vital roles. This article discusses Eigenproblem non-symmetric in well max-plus algebra. By defining certain vector corresponding to...