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Algorithms for Constructing Computably Enumerable Sets

2023-05-23 Computers
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Release : 2023-05-23
Genre : Computers
Kind : eBook
Book Rating : 047/5 ( reviews)

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Book Synopsis Algorithms for Constructing Computably Enumerable Sets by : Kenneth J. Supowit

Download or read book Algorithms for Constructing Computably Enumerable Sets written by Kenneth J. Supowit. This book was released on 2023-05-23. Available in PDF, EPUB and Kindle. Book excerpt: Logicians have developed beautiful algorithmic techniques for the construction of computably enumerable sets. This textbook presents these techniques in a unified way that should appeal to computer scientists. Specifically, the book explains, organizes, and compares various algorithmic techniques used in computability theory (which was formerly called "classical recursion theory"). This area of study has produced some of the most beautiful and subtle algorithms ever developed for any problems. These algorithms are little-known outside of a niche within the mathematical logic community. By presenting them in a style familiar to computer scientists, the intent is to greatly broaden their influence and appeal. Topics and features: · All other books in this field focus on the mathematical results, rather than on the algorithms. · There are many exercises here, most of which relate to details of the algorithms. · The proofs involving priority trees are written here in greater detail, and with more intuition, than can be found elsewhere in the literature. · The algorithms are presented in a pseudocode very similar to that used in textbooks (such as that by Cormen, Leiserson, Rivest, and Stein) on concrete algorithms. · In addition to their aesthetic value, the algorithmic ideas developed for these abstract problems might find applications in more practical areas. Graduate students in computer science or in mathematical logic constitute the primary audience. Furthermore, when the author taught a one-semester graduate course based on this material, a number of advanced undergraduates, majoring in computer science or mathematics or both, took the course and flourished in it. Kenneth J. Supowit is an Associate Professor Emeritus, Department of Computer Science & Engineering, Ohio State University, Columbus, Ohio, US.

Recursively Enumerable Sets and Degrees

1999-11-01 Mathematics
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Release : 1999-11-01
Genre : Mathematics
Kind : eBook
Book Rating : 996/5 ( reviews)

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Book Synopsis Recursively Enumerable Sets and Degrees by : Robert I. Soare

Download or read book Recursively Enumerable Sets and Degrees written by Robert I. Soare. This book was released on 1999-11-01. Available in PDF, EPUB and Kindle. Book excerpt: ..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988

Handbook of Computability Theory

1999-10-01 Mathematics
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Release : 1999-10-01
Genre : Mathematics
Kind : eBook
Book Rating : 043/5 ( reviews)

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Book Synopsis Handbook of Computability Theory by : E.R. Griffor

Download or read book Handbook of Computability Theory written by E.R. Griffor. This book was released on 1999-10-01. Available in PDF, EPUB and Kindle. Book excerpt: The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.

Information and Randomness

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 783/5 ( reviews)

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Book Synopsis Information and Randomness by : Cristian S. Calude

Download or read book Information and Randomness written by Cristian S. Calude. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of the monograph Information and Randomness: An Algorithmic Perspective by Crist ian Calude was published in 1994. In my Foreword I said: "The research in algorithmic information theory is already some 30 years old. However, only the recent years have witnessed a really vigorous growth in this area. . . . The present book by Calude fits very well in our series. Much original research is presented. . . making the approach richer in consequences than the classical one. Remarkably, however, the text is so self-contained and coherent that the book may also serve as a textbook. All proofs are given in the book and, thus, it is not necessary to consult other sources for classroom instruction. " The vigorous growth in the study of algorithmic information theory has continued during the past few years, which is clearly visible in the present second edition. Many new results, examples, exercises and open prob lems have been added. The additions include two entirely new chapters: "Computably Enumerable Random Reals" and "Randomness and Incom pleteness". The really comprehensive new bibliography makes the book very valuable for a researcher. The new results about the characterization of computably enumerable random reals, as well as the fascinating Omega Numbers, should contribute much to the value of the book as a textbook. The author has been directly involved in these results that have appeared in the prestigious journals Nature, New Scientist and Pour la Science.

Computability Theory

2017-09-06 Mathematics
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Release : 2017-09-06
Genre : Mathematics
Kind : eBook
Book Rating : 965/5 ( reviews)

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Book Synopsis Computability Theory by : S. Barry Cooper

Download or read book Computability Theory written by S. Barry Cooper. This book was released on 2017-09-06. Available in PDF, EPUB and Kindle. Book excerpt: Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.

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