Foundations of System Theory: Finitary and Infinitary Conditions

Softcover Nachdruck of the original 1. Auflage 1976
ISBN: 978-3-540-07611-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 115, 99 Seiten, Paperback, Format (B × H): 170 mm x 244 mm, Gewicht: 202 g

Reihe: Lecture Notes in Economics and Mathematical Systems

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].

Zielgruppe

Research

Autoren/Hrsg.

Anderson, Brian D. O.

Manes, E. G.

Arbib, Michael A.

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie

Inhaltsverzeichnis

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.