Theory of Automata deals with mathematical aspects of the theory of automata theory, with emphasis on the finite deterministic automaton as the basic model. All other models, such as finite non-deterministic and probabilistic automata as well as pushdown and linear bounded automata, are treated as generalizations of this basic model. The formalism chosen to describe finite deterministic automata is that of regular expressions. A detailed exposition regarding this formalism is presented by considering the algebra of regular expressions.
This volume is comprised of four chapters and begins with a discussion on finite deterministic automata, paying particular attention to regular and finite languages; analysis and synthesis theorems; equivalence relations induced by languages; sequential machines; sequential functions and relations; definite languages and non-initial automata; and two-way automata. The next chapter describes finite non-deterministic and probabilistic automata and covers theorems concerning stochastic languages; non-regular stochastic languages; and probabilistic sequential machines. The book then introduces the reader to the algebra of regular expressions before concluding with a chapter on formal languages and generalized automata. Theoretical exercises are included, along with ""problems"" at the end of some sections.
This monograph will be a useful resource for beginning graduate or advanced undergraduates of mathematics.

Contenu

Preface
Acknowledgments
Note to the Reader
Chapter I. Finite Deterministic Automata
§ 1. Regular Languages
§ 2. Analysis And Synthesis Theorems
§ 3. Characteristic Equations
§ 4. Equivalence Relations Induced by Languages
§ 5. Sequential Machines
§ 6. Experiments and Minimization
§ 7. Sequential Functions and Relations
§ 8. Definite Languages and Non-Initial Automata
§ 9. Finite Languages
§10. Two-Way Automata
Chapter II. Finite Nonn-Determinintic and Probabilistic Automata
§ 1. Non-Deterministic Automata
§ 2. Probabilistic Automata and Cut-Point Representation
§ 3. Theorems Concerning Stochastic Languages
§ 4. Non-Regular Stochastic Languages
§ 5. Probabilistic Sequential Machines
§ 6. Realizability of Functions
Chapter III. Algebra of Regular Expressions
§ 1. Star Height
§ 2. Solution of Equations
§ 3. The Sets Sr and (Vr. Languages Over a One-Letter Alphabet
§ 4. Languages Containing the Empty Word
§ 5. Commutative Languages
§ 6. Non-Existence of a Finite Basis for the Sets
§ 7. Two Complete Axiom Systems
§ 8. Operators Preserving Regularity
Chapter IV. Formal Languages and Generalized Automata
§ 1. Hierarchy of Languages
§ 2. Type 3 Languages
§ 3. Context-Free Languages
§ 4. Inclusion Relations
§ 5. Pushdown Automata
§ 6. Context-Sensitive Languages and Linear Bounded Automata
§ 7. Type 0 Languages and Turing Machines
§ 8. Infinite-State Machines
§ 9. Abstract Pushdown Automata
§ 10. Regular Canonical Systems
Historical And Bibliographical Remarks
References
Symbol Index
Author Index
Subject Index