Foundations of System Theory: Finitary and Infinitary Conditions (Lecture Notes in Economics and Mathematical Systems, 115)

Anderson, Brian D.O.; Arbib, Michael A.; Manes, E. G.

ISBN 10: 3540076115 / ISBN 13: 9783540076117

Published by Springer, 1976

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Bibliographic Details

• Title: Foundations of System Theory: Finitary and Infinitary Conditions (Lecture Notes in Economics and Mathematical Systems, 115)
• Publisher: Springer
• Publication Date: 1976
• Language: English
• ISBN 10: 3540076115
• ISBN 13: 9783540076117
• Binding: Soft cover
• Condition: New

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Synopsis

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].