Foundations of System Theory: Finitary and Infinitary Conditions

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].

List of contents

1. A General Setting for Discrete Action Nonlinear Systems.- 2. Nerode Equivalence Approach.- 3. Tree Automata: Finite Successes and Infinite Failures.- 4. Finite Step Conditions.- 5. Augmenting the Process.- Conclusions.- References.

Product details

• Authors: Brian D Anderson, Brian D O Anderson, Brian D. O. Anderson, Brian D.O. Anderson, Michael Arbib, Michael A Arbib, Michael A. Arbib, E G Manes, E. G. Manes
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 16.11.2012
• EAN: 9783540076117
• ISBN: 978-3-540-07611-7
• No. of pages: 99
• Dimensions: 172 mm x 242 mm x 7 mm
• Weight: 201 g
• Illustrations: VIII, 99 p.
• Series: Lecture Notes in Economics and Mathematical Systems; Lecture Notes in Economics and Mathematical Systems
• Subject: Social sciences, law, business > Business > Economics