Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks

Overview

This textbook provides an introduction to the fundamental models of massively parallel computation, the most important technique for high-performance computing. It presents a coherent exposition of analytic methods and results for the exploration and understanding of cellular automata and discrete neural networks as computational and dynamical systems.
The book will be useful also as a reference manual to the scattered literature in the field. Each chapter includes a separate ...
See more details below
Paperback (Softcover reprint of the original 1st ed. 1995)
$81.16
BN.com price
(Save 18%)$99.00 List Price
Other sellers (Paperback)
  • All (6) from $79.70   
  • New (5) from $79.70   
  • Used (1) from $141.16   
Sending request ...

Overview

This textbook provides an introduction to the fundamental models of massively parallel computation, the most important technique for high-performance computing. It presents a coherent exposition of analytic methods and results for the exploration and understanding of cellular automata and discrete neural networks as computational and dynamical systems.
The book will be useful also as a reference manual to the scattered literature in the field. Each chapter includes a separate bibliography, as well as pointers to historically relevant papers, and gives exercise problems for the reader.
Read More Show Less

Product Details

  • ISBN-13: 9783642779077
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 2/12/2012
  • Series: Texts in Theoretical Computer Science. An EATCS Series
  • Edition description: Softcover reprint of the original 1st ed. 1995
  • Edition number: 1
  • Pages: 272
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.61 (d)

Table of Contents

1. Turing Computability and Complexity.- 1.1 Models of Sequential Computation.- 1.1.1 A Simple Model: the Finite-State Machine.- 1.1.2 Turing Machines.- 1.2 Complexity.- 1.2.1 Nondeterministic Computations.- 1.2.2 Randomized Algorithms.- 1.2.3 Parallel Computation.- 1.3 Cellular Machines.- 1.4 Prerequisites.- References.- 2. Cellular Automata.- 2.1 Finite-State Automata.- 2.2 Regular Graphs.- 2.3 Local Rules and Global Maps.- 2.3.1 Cellular Spaces.- 2.3.2 Local Rules.- 2.3.3 Global Maps and Dynamical Systems.- 2.4 Fundamental Questions.- 2.5 Notation.- 2.6 Problems.- 2.7 Notes.- References.- 3. Linear Cellular Automata.- 3.1 Linear Rules.- 3.2 Basic Properties.- 3.2.1 Global Injectivity and Surjectivity Modulo m.- 3.2.2 Self-reproduction with Linear Automata.- 3.2.3 Linear Automata on Rings and Semigroups.- 3.3 Global Dynamics via Fractals.- 3.4 The Role of Linear Rules.- 3.5 Problems.- 3.6 Notes.- References.- 4. Semi-totalistic Automata.- 4.1 Semi-totalistic Rules.- 4.1.1 An Example: Conway’s Game of LIFE.- 4.1.2 Nomenclature for Totalistic Rules.- 4.2 Construction and Computation Universality.- 4.2.1 Computation Universality of LIFE.- 4.2.2 Constructibility and Self-reproduction.- 4.2.3 Provable Computation Universality.- 4.3 Restricted Totalistic Rules.- 4.4 Threshold Automata.- 4.5 Problems.- 4.6 Notes.- References.- 5. Decision Problems.- 5.1 Algorithmic and Dynetic Problems.- 5.2 ID Euclidean Automata.- 5.3 2D Euclidean Automata.- 5.3.1 Reversibility is Unsolvable.- 5.3.2 Surjectivity is Unsolvable.- 5.4 Noneuclidean Automata.- 5.5 Complexity Questions.- 5.6 Problems.- 5.7 Notes.- References.- 6. Neural and Random Boolean Networks.- 6.1 Types of Generalizations.- 6.2 Other Parallel Models.- 6.3 Summary of Results.- 6.4 Proofs.- 6.4.1 A Hierarchy.- 6.4.2 A Universal Neural Network.- 6.4.3 Equivalence of Cellular Automata and Neural Networks.- 6.4.4 Equivalence of Neural Networks and Random Networks.- 6.4.5 The Stability Problem is Neurally Unsolvable.- 6.5 Problems.- 6.6 Notes.- References.- 7. General Properties.- 7.1 Metric Preliminaries.- 7.1.1 Metrics and Topologies.- 7.1.2 Convergence and Continuity.- 7.2 Basic Results.- 7.2.1 The Moore-Myhill Theorem.- 7.2.2 Nondeterministic Cellular Automata.- 7.3 Injeetivity, Surjectivity and Local Reversibility.- 7.4 Some Generalizations.- 7.4.1 Neural and Random Networks.- 7.4.2 Combinatorial Generalizations on Euclidean Spaces.- 7.5 Problems.- 7.6 Notes.- References.- 8. Classification.- 8.1 Finite Networks.- 8.1.1 The Difficulties.- 8.1.2 Complexity of Classifying Finite Networks.- 8.2 Wolfram Classification.- 8.3 Classification via Limit Sets.- 8.3.1 Culik-Yu’s Classes and Ishii’s Classes.- 8.3.2 About Entropy.- 8.4 Mean Field Theory.- 8.5 Local Structure Theory.- 8.5.1 Zeroth-order and First-order Local Structure Theories.- 8.5.2 Higher-order Local Structure Theories.- 8.6 Other Classifications.- 8.7 Problems.- 8.8 Notes.- References.- 9. Asymptotic Behavior.- 9.1 Linear Rules.- 9.1.1 Linear Automata on Tori.- 9.1.2 Linear Automata on the Line.- 9.2 Exact Solution.- 9.3 Simulation in Continuous Systems.- 9.3.1 Discrete Computation by Continuous Systems.- 9.3.2 Nonlocal Properties.- 9.3.2.1 The ø-transform.- 9.3.2.2 Sarkovskii’s Theorem.- 9.4 Observability.- 9.4.1 Observability of the Identity.- 9.4.2 Toggle Rules and the Extension Property.- 9.4.3 Observability of Linear Cellular Automata.- 9.4.4 Observability in Neural Networks.- 9.5 Problems.- 9.6 Notes.- References.- 10. Some Inverse Problems.- 10.1 Signals and Synchronization.- 10.1.1 Synchronization of a Line.- 10.1.2 Synchronization of a Network.- 10.1.3 Signals in Dimension 1.- 10.1.4 Clocks.- 10.2 Formal Language Recognition.- 10.2.1 Models.- 10.2.2 A Speedup Theorem.- 10.3 Picture Languages.- 10.3.1 The Issue of Representation.- 10.3.2—-Languages in Spaces of Linear Growth.- 10.3.3 2D-Euclidean Languages.- 10.3.4 Recognition over Spaces of Exponential Growth.- 10.3.5 Recognition over Spaces of Subexponential Growth.- 10.4 Problems.- 10.5 Notes.- References.- 11. Real Computation.- 11.1 Representation and Primitives.- 11.2 Exact Computation.- 11.2.1 Constant-time Computation.- 11.2.2 Variable-time Computation.- 11.3 Approximate Computation by Neural Nets.- 11.3.1 Relative Shadowing.- 11.3.2 Shadowing Bases.- 11.4 Problems.- 11.5 Notes.- References.- 12. A Bibliography of Applications.- 12.1 Physics.- 12.2 Chemistry.- 12.3 Biology.- 12.4 Computer Science.- 12.5 Artificial Intelligence and Cognitive Science.- 12.6 Miscellaneous.- References.- Author Index.- Symbol Index.
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)