Neural Networks and Analog Computation

Beyond the Turing Limit

  • Hava T. Siegelmann

Part of the Progress in Theoretical Computer Science book series (PTCS)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Hava T. Siegelmann
    Pages 1-17
  3. Hava T. Siegelmann
    Pages 19-27
  4. Hava T. Siegelmann
    Pages 29-58
  5. Hava T. Siegelmann
    Pages 59-76
  6. Hava T. Siegelmann
    Pages 77-89
  7. Hava T. Siegelmann
    Pages 91-96
  8. Hava T. Siegelmann
    Pages 97-113
  9. Hava T. Siegelmann
    Pages 115-120
  10. Hava T. Siegelmann
    Pages 121-139
  11. Hava T. Siegelmann
    Pages 141-146
  12. Hava T. Siegelmann
    Pages 147-152
  13. Hava T. Siegelmann
    Pages 153-164
  14. Back Matter
    Pages 165-184

About this book


The theoretical foundations of Neural Networks and Analog Computation conceptualize neural networks as a particular type of computer consisting of multiple assemblies of basic processors interconnected in an intricate structure. Examining these networks under various resource constraints reveals a continuum of computational devices, several of which coincide with well-known classical models. What emerges is a Church-Turing-like thesis, applied to the field of analog computation, which features the neural network model in place of the digital Turing machine. This new concept can serve as a point of departure for the development of alternative, supra-Turing, computational theories. On a mathematical level, the treatment of neural computations enriches the theory of computation but also explicated the computational complexity associated with biological networks, adaptive engineering tools, and related models from the fields of control theory and nonlinear dynamics.

The topics covered in this work will appeal to a wide readership from a variety of disciplines. Special care has been taken to explain the theory clearly and concisely. The first chapter review s the fundamental terms of modern computational theory from the point of view of neural networks and serves as a reference for the remainder of the book. Each of the subsequent chapters opens with introductory material and proceeds to explain the chapter’s connection to the development of the theory. Thereafter, the concept is defined in mathematical terms.

Although the notion of a neural network essentially arises from biology, many engineering applications have been found through highly idealized and simplified models of neuron behavior. Particular areas of application have been as diverse as explosives detection in airport security, signature verification, financial and medical times series prediction, vision, speech processing, robotics, nonlinear control, and signal processing. The focus in all of these models is entirely on the behavior of networks as computer.

The material in this book will be of interest to researchers in a variety of engineering and applied sciences disciplines. In addition, the work may provide the base of a graduate-level seminar in neural networks for computer science students.


Natur Theorie complexity computer science development model robot robotics science simulation

Authors and affiliations

  • Hava T. Siegelmann
    • 1
  1. 1.Department of Information Systems EngineeringFaculty of Industrial Engineering and Management TechnionHaifaIsrael

Bibliographic information