Computation and Automata (Encyclopedia of Mathematics and its Applications, Series Number 25)

In This Book, Which Was Originally Published In 1985, Arto Salomaa Gives An Introduction To Certain Mathematical Topics Central To Theoretical Computer Science: Computability And Recursive Functions, Formal Languages And Automata, Computational Complexity And Cryptography. Without Sacrificing Readability, The Presentation Is Essentially Self-contained, With Detailed Proofs Of All Statements Provided. Professor Salomaa Is Well Known For His Books In This Area. The Present Work Provides An Insight Into The Basics, Together With Explanations Of Some Of The More Important Developments In The Field. Introduction : Models Of Computation -- Rudiments Of Language Theory -- Restricted Automata -- Turing Machines And Recursive Functions -- Famous Decision Problems -- Computational Complexity -- Cryptography -- Trends In Automata And Language Theory. Arto Salomaa. Includes Index. Bibliography: P. 269-277. Cover; Half Title; Series Page; Title; Copyright; Contents; Editor's Statement; Foreword; Acknowledgments; Chapter 1 Introduction: Models of Computation; Chapter 2 Rudiments of Language Theory; 2.1. LANGUAGES AND REWRITING SYSTEMS; 2.2. GRAMMARS; 2.3. POST SYSTEMS; 2.4. MARKOV ALGORITHMS; 2.5. L SYSTEMS; EXERCISES; Chapter 3 Restricted Automata; 3.1. FINITE AUTOMATA; 3.2. KLEENE CHARACTERIZATION; 3.3. GENERALIZED SEQUENTIAL MACHINES; 3.4. PUMPING LEMMAS; 3.5. PUSHDOWN AUTOMATA; EXERCISES; Chapter 4 Turing Machines and Recursive Functions; 4.1. A GENERAL MODEL OF COMPUTATION This introduction to certain mathematical topics central to theoretical computer science treats computability and recursive functions, formal languages and automata, computational complexity, and cruptography. The presentation is essentially self-contained with detailed proofs of all statements provided. Although it begins with the basics, it proceeds to some of the most important recent developments in theoretical computer science. This 1979 book shows how differential equation theory can be beautifully simplified by treating such equations from the product integral viewpoint. The first chapter, dealing with linear ordinary differential equations, is accessible to anyone with a knowledge of matrix theory and elementary calculus. Later chapters assume a more sophisticated reader. In this text, which was originally published in 1985, Arto Salomaa gives an introduction to certain mathematical topics central to theoretical computer science: computability and recursive functions, formal languages and automata, computational complexity and cryptography