Ebook: 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].

---

---

Content:
Front Matter....Pages N1-VII
A General Setting for Discrete Action Nonlinear Systems....Pages 1-26
Nerode Equivalence Approach....Pages 27-42
Tree Automata: Finite Successes and Infinite Failures....Pages 43-62
Finite Step Conditions....Pages 63-80
Augmenting the Process....Pages 81-88
Conclusions....Pages 89-91
Back Matter....Pages 92-97

---

Content:
Front Matter....Pages N1-VII
A General Setting for Discrete Action Nonlinear Systems....Pages 1-26
Nerode Equivalence Approach....Pages 27-42
Tree Automata: Finite Successes and Infinite Failures....Pages 43-62
Finite Step Conditions....Pages 63-80
Augmenting the Process....Pages 81-88
Conclusions....Pages 89-91
Back Matter....Pages 92-97
....