Foundations of System Theory Finitary and Infinitary Conditions |
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| Author:
| Anderson, Brian D. O.
Arbib, Michael A.
Manes, E. G. |
| Series title: | Lecture Notes in Economics and Mathematical Systems Ser. |
| ISBN: | 978-3-540-07611-7 |
| Publication Date: | Mar 1976 |
| Publisher: | Springer Berlin / Heidelberg
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| Imprint: | Springer |
| Book Format: | Paperback |
| List Price: | USD $54.99 |
Book Description:
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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...
More DescriptionThis 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].