User:Whiteknight/Automata Theory

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This page is an outline for a proposed book or project. This is only a planning page, not an actual book.
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This outline was last edited on 2 November 2010. Last edit over 49 months ago. Please update.

(Whiteknight) (Discuss) (Book Foundry) (Current Books) (VBD Edit)

This outline will serve to fill a hole in available material here on wikibooks. I would like this book to be a precursor to the Cellular Automata book, and as the necessary companion material to other books on periphery topics such as Compiler construction, etc. Also, this would serve as a good theoretical basis for my future book on Lex and Yacc.

I intend to shelve this book on the mathematics bookshelf, even though I am well aware that most of the uses of Automata theory will be found on the CS bookshelf.

Introduction[edit]

This book is going to consider the topic of Automata Theory, Sequential Machines, and Artificial Languages. The goal of this book is to become a solid foundational work for topics that are based off the automata theory framework.

Table of Contents[edit]

  • Abstract Algebra
    • Basic introduction
    • Development of key terms and notation
    • Redirection to Abstract algebra
  • Sequential Machines
    • What are Sequential Machines
    • Mealy Machines
    • Moore Machines
    • Machine Equivalence
    • Incompletely specified machines
  • Decomposition of Machines
    • Interconnection of Sequential Machines
    • Composite Machines
    • Partitioning
    • Covering
  • Measurement and Control
    • Terminal State identification
    • Finite Memory Machines
    • Initial State Identification
    • Information-lossless Machines
    • Machine Identification
    • Redirect to Control Systems
  • Regular Expressions
    • Relationships between input and machine state
    • Regular Expressions Introduction
    • Regular Expressions and state diagrams
    • Redirection to Regular Expressions
  • Vectors and Linear Transforms
    • Vector Spaces
    • Linear Transforms
    • Canonical Representation
    • Invariant Factors
    • Redirect to Linear algebra
  • Linear Sequential Machines
    • Representing Linear Machines
    • Equivalent Linear Machines
    • Autonomous Response
    • Sequential Networks
    • Transfer Functions
  • Turing Machines
    • Turing Machines Introduction
    • Programing turing Machines
    • Recursive Functions
    • Predicates
    • Computability
    • Enumerable Sets
  • Artificial Languages
    • Languages
    • Phase-Structure Grammars
    • Language Operations
    • Decision Problems
    • Redirect to Compiler construction

Resources[edit]

Original outline based off the following book:

  • Booth, Taylor L. "Sequential Machines and Automata Theory", John Wiley and Sons, New York, 1967.

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Automata Theory =Abstract Algebra

  • Abstract Algebra Introduction
  • Terms and Notations

=Sequential Machines

  • Sequential Machines Introduction
  • Mealy Machines
  • Moore Machines
  • Machine Equivalence
  • Incompletely Specified Machines

=Decomposition of Machines

  • Interconnection of Sequential Machines
  • Composite Machines
  • Partitioning
  • Covering

=Measurement and Control

  • Terminal State Identification
  • Finite Memory Machines
  • Initial State Identification
  • Information-Lossless Machines
  • Machine Identfication

=Regular Expressions

  • Regular Expression Introduction
  • Relationships Between Input and State
  • Regular Expression State Diagrams

=Vectors and Linear Transforms

  • Vector Spaces
  • Linear Transforms
  • Canonical Representation
  • Invariant Factors

=Linear Sequential Machines

  • Representing Linear Machines
  • Equivalent Linear Machines
  • Autonomous Response
  • Sequential Networks
  • Transfer Functions

=Turing Machines

  • Turing Machines Introduction
  • Programming Turing Machines
  • Recursive Functions
  • Predicates
  • Computability
  • Enumerable Sets

=Artificial Languages

  • Languages Introduction
  • Phase-Structure Grammars
  • Language Operations
  • Decision Problems


End of outline. Below this point is normal text and can be edited like normal.