# On the complexity of the boolean minimal realization problem in the max-plus algebra∗

• Published 1997

#### Abstract

One of the open problems in the max-plus-algebraic system theory for discrete event systems is the minimal realization problem. We consider 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 maxplus-algebraic identity element. We show that the corresponding decision problem (i.e., deciding whether or not a boolean realization of a given order exists) is decidable, and that the boolean minimal realization problem can be solved in a number of elementary operations that is bounded from above by an exponential of the square of (any upper bound of) the minimal system order.

### Cite this paper

@inproceedings{Schutter1997OnTC, title={On the complexity of the boolean minimal realization problem in the max-plus algebra∗}, author={Bart De Schutter and Bart De Moor}, year={1997} }