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Foundations of System Theory: Finitary and Infinitary Conditions

  • Book
  • © 1976

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Authors:
  1. Brian D. O. Anderson

    1. Department of Electrical Engineering, University of Newcastle, Australia

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  2. Michael A. Arbib

    1. Department of Computer and Information Science, University of Massachusetts, Amherst, USA

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  3. Ernest G. Manes

    1. Department of Mathematics, University of Massachusetts, Amherst, USA

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

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Table of contents (6 chapters)

  1. Front Matter

    Pages N1-VII
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  2. A General Setting for Discrete Action Nonlinear Systems

    • Brian D. O. Anderson, Michael A. Arbib, Ernest G. Manes
    Pages 1-26

  3. Nerode Equivalence Approach

    • Brian D. O. Anderson, Michael A. Arbib, Ernest G. Manes
    Pages 27-42

  4. Tree Automata: Finite Successes and Infinite Failures

    • Brian D. O. Anderson, Michael A. Arbib, Ernest G. Manes
    Pages 43-62

  5. Finite Step Conditions

    • Brian D. O. Anderson, Michael A. Arbib, Ernest G. Manes
    Pages 63-80

  6. Augmenting the Process

    • Brian D. O. Anderson, Michael A. Arbib, Ernest G. Manes
    Pages 81-88

  7. Conclusions

    • Brian D. O. Anderson, Michael A. Arbib, Ernest G. Manes
    Pages 89-91

  8. Back Matter

    Pages 92-97
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Keywords

About this book

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].

Authors and Affiliations

  • Department of Electrical Engineering, University of Newcastle, Australia

    Brian D. O. Anderson

  • Department of Computer and Information Science, University of Massachusetts, Amherst, USA

    Michael A. Arbib

  • Department of Mathematics, University of Massachusetts, Amherst, USA

    Ernest G. Manes

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