The purpose of this work is to introduce and study the concept of minimal deterministic automaton with IF-outputs which realizes the given IF-language. Among two methods for construction of such automaton presented here, one is based on Myhill-Nerode’s theory while the other is based on derivatives of the given IF-language. Meanwhile, the categories of deterministic automata with IF-outputs and...

We introduce a robust statistical approach to realization from Minimal Recursion Semantics representations. The approach treats realization as a translation problem, transforming the Dependency MRS graph representation to a surface string. Translation is based on a Synchronous Context-Free Grammar that is automatically extracted from a large corpus of parsed sentences. We have evaluated the new...

In this paper, we state the positive real lemma and the strictly positive real lemma (KYP lemma) for non-minimal realization systems. First we show the positive real lemma for stabilizable and observable systems under only the constraint on the regularity of the systems, by using the generalized algebraic Riccati equation. Moreover we show that the solution of the Lyapunov equation in the posit...

A solution is presented for the problem of realizing a minimal state-space model of an LTI discrete-time system from a partial expansion in terms of generalized orthonormal basis functions, also known as Hambo basis functions. For the solution of the minimal partial realization problem fruitful use is made of the Hambo operator transform theory that underlies the basis function expansion. The r...

In this paper we describe a complete parameterization of the solutions to the partial stochastic realization problem in terms of a nonstandard matrix Riccati equation. Our analysis of this Covariance Extension Equation is based on a recent complete parameterization of all strictly positive real solutions to the rational covariance extension problem, answering a conjecture due to Georgiou in the...

The solutions of the partial realization problem have to satisfy a finite number of interpolation conditions at 1. The minimal degree of an interpolating deterministic system is called the algebraic degree or McMillan degree of the partial covariance sequence and is easy to compute. The solutions of the partial stochastic realization problem have to satisfy the same interpolation conditions and...

we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.

Extraction of low-dimensional latent space from high-dimensional observation data is essential to construct a real-time robot controller with world model on the extracted space. However, there no established method for tuning dimension size automatically, suffering finding necessary and sufficient size, i.e. minimal realization model. In this study, we analyze improve Tsallis-based variational ...