Download or read book Indivisible Characteristics of Recursively Enumerable Sets written by Ellen S. Chih and published by . This book was released on 2015 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: A split of an r.e. set A is a pair of disjoint r.e. sets whose union is A. We investigate information theoretic properties of r.e. sets and properties of their enumerations, and whether these properties are preserved under splittings. The first part is involved with dynamic notions. An r.e. set is speedable if for every computable function, there exists a finite algorithm enumerating membership faster, by the desired computable factor, on infinitely many integers. Remmel (1986) asked whether every speedable set could be split into two speedable sets. Jahn published a proof, answering their question positively. However, his proof was seen to be incorrect and we construct a speedable set that cannot be split into speedable sets, answering their question negatively. We also prove additional splitting results related to speedability. The second part is involved with effectively closed sets. We introduce the notion of being recursively avoiding and prove several results.
Download or read book Complexity Properties of Recursively Enumerable Sets written by Ivan da Costa Marques and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Properties of Recursively Enumerable Sets Uniform for Equivalence Relations written by Hong Ye and published by . This book was released on 1988 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recursively Enumerable Sets and Degrees written by Robert I. Soare and published by Springer Science & Business Media. This book was released on 1987 with total page 464 pages. 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
Download or read book Automorphisms of the Lattice of Recursively Enumerable Sets written by Peter Abe Cholak and published by American Mathematical Soc.. This book was released on 1991 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Structural Learning Volume 1 written by Joseph M. Scandura and published by Routledge. This book was released on 2017-09-13 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1973, this book was published in two volumes. In the first volume, the author describes what he sees as the rudiments of three deterministic partial theories of structural learning. The first involves competence, partial theories which deal only with the problem of how to account for the various kinds of behavior of which people are typically capable. Special attention is given to mathematical competence. Nothing is said about learning or performance. The second partial theory is concerned with motivation, learning, and performance under idealized conditions, and is obtained from the first partial theory by imposing further structure on it. This theory says nothing about memory of the limited capacity of human subjects to process information. ... The final theory is obtained from the second by making additional assumptions, which bring memory and finite information processing into the picture. The theory is still partial, however, since no attempt is made to deal with certain ultra-short-term behavioral phenomena which appear to depend directly on particular physiological characteristics.
Download or read book Recursively enumerable sets and degerees written by R.I.·索尔 (美) and published by . This book was released on 1987 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Note on Recursively Enumerable Sets and Computable Functions written by 陳昭瑋 and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Computer Science written by K. L. P. Mishra and published by PHI Learning Pvt. Ltd.. This book was released on 2006-01-01 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Third Edition, in response to the enthusiastic reception given by academia and students to the previous edition, offers a cohesive presentation of all aspects of theoretical computer science, namely automata, formal languages, computability, and complexity. Besides, it includes coverage of mathematical preliminaries. NEW TO THIS EDITION • Expanded sections on pigeonhole principle and the principle of induction (both in Chapter 2) • A rigorous proof of Kleene’s theorem (Chapter 5) • Major changes in the chapter on Turing machines (TMs) – A new section on high-level description of TMs – Techniques for the construction of TMs – Multitape TM and nondeterministic TM • A new chapter (Chapter 10) on decidability and recursively enumerable languages • A new chapter (Chapter 12) on complexity theory and NP-complete problems • A section on quantum computation in Chapter 12. • KEY FEATURES • Objective-type questions in each chapter—with answers provided at the end of the book. • Eighty-three additional solved examples—added as Supplementary Examples in each chapter. • Detailed solutions at the end of the book to chapter-end exercises. The book is designed to meet the needs of the undergraduate and postgraduate students of computer science and engineering as well as those of the students offering courses in computer applications.
Download or read book Languages and Machines written by Thomas A. Sudkamp and published by Pearson Education India. This book was released on 2008 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elements of Set Theory written by Herbert B. Enderton and published by Academic Press. This book was released on 1977-05-23 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Download or read book Philosophy of Mathematics written by and published by Elsevier. This book was released on 2009-07-08 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics-Clearly written expositions of fundamental ideas and concepts-Definitive discussions by leading researchers in the field-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included
Download or read book What Can Be Computed written by John MacCormick and published by Princeton University Press. This book was released on 2018-05-01 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible and rigorous textbook for introducing undergraduates to computer science theory What Can Be Computed? is a uniquely accessible yet rigorous introduction to the most profound ideas at the heart of computer science. Crafted specifically for undergraduates who are studying the subject for the first time, and requiring minimal prerequisites, the book focuses on the essential fundamentals of computer science theory and features a practical approach that uses real computer programs (Python and Java) and encourages active experimentation. It is also ideal for self-study and reference. The book covers the standard topics in the theory of computation, including Turing machines and finite automata, universal computation, nondeterminism, Turing and Karp reductions, undecidability, time-complexity classes such as P and NP, and NP-completeness, including the Cook-Levin Theorem. But the book also provides a broader view of computer science and its historical development, with discussions of Turing's original 1936 computing machines, the connections between undecidability and Gödel's incompleteness theorem, and Karp's famous set of twenty-one NP-complete problems. Throughout, the book recasts traditional computer science concepts by considering how computer programs are used to solve real problems. Standard theorems are stated and proven with full mathematical rigor, but motivation and understanding are enhanced by considering concrete implementations. The book's examples and other content allow readers to view demonstrations of—and to experiment with—a wide selection of the topics it covers. The result is an ideal text for an introduction to the theory of computation. An accessible and rigorous introduction to the essential fundamentals of computer science theory, written specifically for undergraduates taking introduction to the theory of computation Features a practical, interactive approach using real computer programs (Python in the text, with forthcoming Java alternatives online) to enhance motivation and understanding Gives equal emphasis to computability and complexity Includes special topics that demonstrate the profound nature of key ideas in the theory of computation Lecture slides and Python programs are available at whatcanbecomputed.com
Download or read book 25th Annual Symposium on Foundations of Computer Science written by IEEE Computer Society. Technical Committee on Mathematical Foundations of Computing and published by . This book was released on 1984 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Journal of Symbolic Logic written by Alonzo Church and published by . This book was released on 1979 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes lists of members.
Download or read book Free Trade Reimagined written by Roberto Mangabeira Unger and published by Princeton University Press. This book was released on 2010-01-04 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Free Trade Reimagined begins with a sustained criticism of the heart of the emerging world economy, the theory and practice of free trade. Roberto Mangabeira Unger does not, however, defend protectionism against free trade. Instead, he attacks and revises the terms on which the traditional debate between free traders and protectionists has been joined. Unger's intervention in this major contemporary debate serves as a point of departure for a proposal to rethink the basic ideas with which we explain economic activity. He suggests, by example as well as by theory, a way of understanding contemporary economies that is both more realistic and more revealing of hidden possibilities for transformation than are the established forms of economics. One message of the book is that we need not choose between accepting and rejecting globalization; we can have a different globalization. Traditional free trade doctrine rests on shaky empirical and theoretical ground. Unger takes a new approach to show when international trade is likely to be useful or harmful to the socially inclusive economic growth that every nation wants. Another message is that the movement of people and ideas is more important than the movement of things and money, and that freedom to change the institutions defining a market economy is just as important as freedom to exchange goods on the basis of those institutions. Free Trade Reimagined ranges broadly within and outside economics. Presenting technical issues in plain language, it appeals to the general reader. It puts a disciplined imagination in the service of rebellion against the dictatorship of no alternatives that characterizes life and thought today.
Download or read book A Mathematical Introduction to Logic written by Herbert B. Enderton and published by Elsevier. This book was released on 2001-01-23 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mathematical Introduction to Logic
