Applied Automata Theory

List of Contributors

Preface

Algebraic Foundations for Automata Theory

1. Semigroups

2. Groups and Homomorphisms

3. Partially Ordered Sets and Lattices

4. Congruences and Other Relations

An Introduction t o Regular Expressions

1. Introduction

2. Definitions

3. Some Laws

4. Historical Remarks

5. Establishing Equations

6. Proof by Reparsing

7. Logical Systems

8. Graph Manipulation

9. Star Height

References

Stochastic Automata and Discrete Systems Theory

1. Introduction

2. Finite Automata

3. Characterization of Stochastic Automata

4. State Probabilities and z-Transform Analysis

5. Multistage Decision Process

6. Entropy of a Stochastic Automaton

7. Unreliable Finite Automaton

8. Eigenvalues of a Stochastic Automaton

Bibliography

Switching Networks as Models of Discrete Stochastic Processes

1. Introduction

2. Introduction to Discrete Probability Theory

3. Some Current Research in Stochastic Sequential Machine Theory

4. On the Synthesis of Stochastic Sequential Machines

5. Applications

References

Bibliography

Bibliography on Random Numbers

Applications of Automata Theory in Coding

1. Introduction

2. Autonomous Linear Sequential Circuits and Cyclic Codes

3. Driven Linear Sequential Circuits and Convolutional Codes

4. Automata Stability and Error Propagation

5. State-Observability, State-Controllability, and Burst-Correction

6. Feed-Forward Inverses and Convolutional Codes

7. Concluding Remarks

References

Content Addressable and Distributed Logic Memories

1. Introduction

2. The Woven Cryotron Memory

3. Associative Memories

4. The Cell Memory

5. The Two-Dimensional Distributed Logic Memory

6. Distributed Logic Computer Systems

References

Recursive Functions and Switching-Circuit Theory

1. Introduction

2. Sets, Cardinality, and the Natural Numbers

3. Computability and the Turing Machine

4. Recursive Functions and Switching Circuits

References

Synthesis of a Cellular Computer

1. Introduction

2. The Twenty-Nine-State Model

3. The Memory Assembly

4. The Nontransfer Instruction Assembly

5. The Transfer Instruction Assembly

6. A Crossover Network

7. The Cellular Machine

8. Physical Considerations

References

Fundamentals of Threshold Logic

1. Introduction

2. Monotonicity Theory

3. Test Synthesis

4. Synthesis of Nets

Appendix A: Integral-Minimal One-Realizations of Five-Argument Threshold Functions

Appendix B: Realizations and Chow Parameters for Six-Argument Threshold Functions

References

Author Index

Subject Index