A Control-Oriented Notion of Finite State Approximation

A Notion of Approximation for Systems over Finite Alphabets

We consider the problem of approximating plants with discrete sensors and actuators (termed ‘systems over finite alphabets’) by deterministic finite memory systems for the purpose of certified-by-design controller synthesis. We propose a new, control-oriented notion of input/output approximation for these systems, that builds on ideas from robust control theory and behavioral systems theory. We...

Fuzzy Best Simultaneous Approximation of a Finite Numbers of Functions

Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.

Finite-State Approximation of Phrase Structure Grammars

Phrase-structure grammars are effective models for important syntactic and semantic aspects of natural languages, but can be computationally too demanding for use as language models in real-time speech recognition. Therefore, finite-state models are used instead, even though they lack expressive power. To reconcile those two alternatives, we designed an algorithm to compute finite-state approxi...

Finite-state subset approximation of phrase structure

We describe a method and a software tool to approximate and manipulate phrase structure grammars by a string representation of derivation trees and an encoding of a finite automaton that recognizes such strings. Many linguistically natural extensions to phrase structure grammars can be modeled on top of the approximation, allowing for a generic mechanism to model parsing and generation of a var...

Convergence of a Finite Element Approximation to a State-Constrained Elliptic Control Problem