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© 1976

Foundations of System Theory: Finitary and Infinitary Conditions

Book

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

  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

  • Book Title Foundations of System Theory: Finitary and Infinitary Conditions
  • Authors Brian D.O. Anderson
    Michael A. Arbib
    E. G. Manes
  • Series Title Lecture Notes in Economics and Mathematical Systems
  • 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
  • Softcover ISBN 978-3-540-07611-7
  • eBook ISBN 978-3-642-45479-0
  • Series ISSN 0075-8442
  • Edition Number 1
  • Number of Pages VIII, 99
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Economic Theory/Quantitative Economics/Mathematical Methods
    Mathematics, general
  • Buy this book on publisher's site
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