Applied Automata Theory
- 1st Edition - January 1, 1968
- Imprint: Academic Press
- Editor: Julius T. Tou
- Language: English
- Hardback ISBN:9 7 8 - 1 - 4 8 3 2 - 0 0 1 6 - 3
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 1 1 7 6 - 3
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 2 5 1 9 - 7
Applied Automata Theory provides an engineering style of presentation of some of the applied work in the field of automata theory. Topics covered range from algebraic foundations… Read more
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Request a sales quoteApplied Automata Theory provides an engineering style of presentation of some of the applied work in the field of automata theory. Topics covered range from algebraic foundations and recursive functions to regular expressions, threshold logic, and switching circuits. Coding problems and stochastic processes are also discussed, along with content addressable memories, probabilistic reliability, and Turing machines. Much emphasis is placed on engineering applications. Comprised of nine chapters, this book first deals with the algebraic foundations of automata theory, focusing on concepts such as semigroups, groups and homomorphisms, and partially ordered sets and lattices, as well as congruences and other relations. The reader is then introduced to regular expressions; stochastic automata and discrete systems theory; and switching networks as models of discrete stochastic processes. Subsequent chapters explore applications of automata theory in coding; content addressable and distributed logic memories; recursive functions and switching-circuit theory; and synthesis of a cellular computer. The book concludes with an assessment of the fundamentals of threshold logic. This monograph is intended for graduates or advanced undergraduates taking a course in information science or a course on discrete systems in modern engineering curriculum.
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
- Edition: 1
- Published: January 1, 1968
- No. of pages (eBook): 342
- Imprint: Academic Press
- Language: English
- Hardback ISBN: 9781483200163
- Paperback ISBN: 9781483211763
- eBook ISBN: 9781483225197
JT
Julius T. Tou
Affiliations and expertise
Computer Sciences Laboratory The Technological Institute
Northwestern University, Evanston, IllinoisRead Applied Automata Theory on ScienceDirect