B. De Schutter and B. De Moor, "On the boolean minimal realization problem in the max-plus algebra," Proceedings of the 4th International Workshop on Discrete Event Systems (WODES'98), Cagliari, Italy, pp. 231-236, Aug. 1998.
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 which the entries of the system matrices are either equal to the max-plus-algebraic zero element or to the max-plus-algebraic identity element.