Advertisement

Foundations of System Theory: Finitary and Infinitary Conditions

  • Brian D. O. Anderson
  • Michael A. Arbib
  • Ernest G. Manes

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 115)

Table of contents

  1. Front Matter
    Pages N1-VII
  2. Brian D. O. Anderson, Michael A. Arbib, Ernest G. Manes
    Pages 1-26
  3. Brian D. O. Anderson, Michael A. Arbib, Ernest G. Manes
    Pages 27-42
  4. Brian D. O. Anderson, Michael A. Arbib, Ernest G. Manes
    Pages 43-62
  5. Brian D. O. Anderson, Michael A. Arbib, Ernest G. Manes
    Pages 63-80
  6. Brian D. O. Anderson, Michael A. Arbib, Ernest G. Manes
    Pages 81-88
  7. Brian D. O. Anderson, Michael A. Arbib, Ernest G. Manes
    Pages 89-91
  8. Back Matter
    Pages 92-97

About this book

Introduction

This paper is one of a series in which the ideas of category theory are applied to problems of system theory. As with the three principal earlier papers, [1-3], the emphasis is on study of the realization problem, or the problem of associating with an input-output description of a system an internal description with something analogous to a state-space. In this paper, several sorts of machines will be discussed, which arrange themselves in the following hierarchy: Input process Machine Output process (Tree automaton) Machine ~ ~ State-behavior Machine I Adjoint Machine .(Sequential Machine) ., I Decomposable Machine (Linear System, Group Machine) Each member of the hierarchy includes members below it; examples are included in parentheaes, and each example is at its lowest possible point in the hierarchy. There are contrived examples of output process machines and IV state-behavior machines which are not adjoint machines [3], but as yet, no examples with the accepted stature of linear systems [4], group machines [5, 6], sequential machines [7, Ch. 2], and tree automata [7, Ch. 4].

Keywords

Finite Nonlinear system category theory foundation system systems theory

Authors and affiliations

  • Brian D. O. Anderson
    • 1
  • Michael A. Arbib
    • 2
  • Ernest G. Manes
    • 3
  1. 1.Department of Electrical EngineeringUniversity of NewcastleAustralia
  2. 2.Department of Computer and Information ScienceUniversity of MassachusettsAmherstUSA
  3. 3.Department of MathematicsUniversity of MassachusettsAmherstUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-45479-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1976
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-07611-7
  • Online ISBN 978-3-642-45479-0
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site