Foundations of System Theory: Finitary and Infinitary Conditions

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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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].

• Finite
• Nonlinear system
• category theory
• foundation
• system
• systems theory

• 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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