Logic, Automata, and Algorithms

✍ Scribed by Mark A. Aiserman, Leonid A. Gusev, Lev I. Rozonoer, Irina M. Smirnova and Aleksey A. Tal' (Eds.)

• Publisher: AP
• Year: 1971
• Tongue: English
• Leaves: 444
• Series: Mathematics in Science and Engineering 79
• Category: Library

✦ Synopsis

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering

✦ Table of Contents

Content:
Edited by
Page iii

Copyright page
Page iv

Preface
Pages ix-x

Translator's Note
Page x

Introduction
Pages xi-xii

1 Elements of Mathematical Logic
Pages 1-26

2 Engineering Applications of Propositional Calculus
Pages 27-57

3 Finite Automata and Sequential Machines: Basic Concepts
Pages 58-85

4 Abstract Structure and Nets
Pages 86-115

5 Technical Embodiment of Finite Automata and Sequential Machines
Pages 116-143

6 Autonomous Finite Automata and Sequential Machines
Pages 144-158

7 Representation of Events in Finite Automata and Sequential Machines
Pages 159-186

8 Recognition of Realizability of a Given Specification. Abstract Synthesis of Finite Automata and Sequential Machines
Pages 187-218

9 Equivalence and Minimization of Sequential Machines
Pages 219-259

10 Transformation of Clock Rates of Sequential Machines
Pages 260-283

11 Determination of the Properties of Sequential Machines from Their Response to Finite Input Sequences
Pages 284-303

12 Algorithms
Pages 304-354

13 Turing Machines
Pages 355-376

Conclusion
Pages 377-385

Problems
Pages 386-408

Bibliography Review Article
Pages 409-426

Addenda to Bibliography Review Article
Pages 427-429

Index
Pages 430-433