The problem of computing minimal realizations of a singular system decomposed into a standard dynamical system and a static system of a given improper transfer matrix is formulated and solved. A new notion of the minimal dynamical-static realization is introduced. It is shown that there always exists a minimal dynamical-static realization of a given improper transfer matrix. A procedure for the...

The context of this article is the program to study the bicategory of spans of graphs as an algebra of processes, with applications to concurrency theory. The objective here is to study functorial aspects of reachability, minimization and minimal realization. The compositionality of minimization has application to model-checking.

Comprehension and corpus studies have found that the tendency to minimize dependency length has a strong influence on constituent ordering choices. In this paper, we investigate dependency length minimization in the context of discriminative realization ranking, focusing on its potential to eliminate egregious ordering errors as well as better match the distributional characteristics of sentenc...

This paper examines the realization of acausal weighting patterns with two-point boundary-value descriptor systems (TPBVDSs). We restrict our attention to the subclass of TPBVDSs which are extendible, i.e., whose input-output weighting pattern can be extended outwards indefinitely, and stationary, so that their weighting pattern is shift-invariant. Then, given an infinite acausal shift-invarian...

The study of realizations of response maps is a topic of control and system theory. Realization theory is used in system identification and control synthesis. A minimal rational realization of a given response map p is a rational realization of p such that the dimension of its state space equals the transcendence degree of the observation field of p. We relate minimality of rational realization...

Algorithms for sliding block codes | an application of symbolic dynamics to information theory, IEEE Trans. then (w; x)j (?1;0) (w; x)j 0;1) 2 B s. The external behavior of a state realization is the system (Z; W; B) where B = fw : (w; x) 2 B s for some xg. The state realization may be regarded as a presentation of its external behavior, with the elements of X as states. A state realization of ...

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 ...