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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 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
Algebraic Foundations for Automata Theory
2. Groups and Homomorphisms
3. Partially Ordered Sets and Lattices
4. Congruences and Other Relations
An Introduction t o Regular Expressions
3. Some Laws
4. Historical Remarks
5. Establishing Equations
6. Proof by Reparsing
7. Logical Systems
8. Graph Manipulation
9. Star Height
Stochastic Automata and Discrete Systems Theory
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
Switching Networks as Models of Discrete Stochastic Processes
2. Introduction to Discrete Probability Theory
3. Some Current Research in Stochastic Sequential Machine Theory
4. On the Synthesis of Stochastic Sequential Machines
Bibliography on Random Numbers
Applications of Automata Theory in Coding
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
Content Addressable and Distributed Logic Memories
2. The Woven Cryotron Memory
3. Associative Memories
4. The Cell Memory
5. The Two-Dimensional Distributed Logic Memory
6. Distributed Logic Computer Systems
Recursive Functions and Switching-Circuit Theory
2. Sets, Cardinality, and the Natural Numbers
3. Computability and the Turing Machine
4. Recursive Functions and Switching Circuits
Synthesis of a Cellular Computer
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
Fundamentals of Threshold Logic
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
- No. of pages:
- © Academic Press 1968
- 1st January 1968
- Academic Press
- eBook ISBN:
Computer Sciences Laboratory The Technological Institute Northwestern University, Evanston, Illinois
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