CONCERNING AN ALGEBRAIC THEORY OF SYSTEMS,

Abstract

There exists a definite trend in engineering to undertake the design and study of systems of increasing size and complexity. In this, there are encountered practical difficulties which suggest the need for a mathematical theory of systems possessing considerably greater generality and conceptual power than existing theories. It appears that such a general, unified theory of systems can be developed along definite algebraic lines. This is so because essentially all of the mathematical models being used for the study of systems of various kinds have a common abstract structure. The purpose of the presentation is to display this abstract structure in terms of an algebraic formalism, and to discuss the applicability of such theory as is developed around it. In particular, it is demonstrated that the proposed theory unifies and, through axiomatic development, subsumes automata theory, the theory of Turing machines, and the input-output theory of systems defined by sets of differential equations and difference equations. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1965
Accession Number
AD0623723

Entities

People

  • Thomas G. Windeknecht

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DTIC Thesaurus Topics

  • Abstracts
  • Automata
  • Automata Theory
  • Difference Equations
  • Differential Equations
  • Engineering
  • Equations
  • Machines
  • Mathematical Models
  • Mathematics
  • Models

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  • Theoretical Analysis.