Enumerability Decidability Computability

Download Enumerability Decidability Computability full books in PDF, epub, and Kindle. Read online Enumerability Decidability Computability ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Enumerability · Decidability Computability

Author : Hans Hermes
Publisher : Springer Science & Business Media
ISBN 13 : 3642461786
Total Pages : 260 pages
Book Rating : 4.6/5 (424 download)

DOWNLOAD NOW!

Book Synopsis Enumerability · Decidability Computability by : Hans Hermes

Download or read book Enumerability · Decidability Computability written by Hans Hermes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Once we have accepted a precise replacement of the concept of algo rithm, it becomes possible to attempt the problem whether there exist well-defined collections of problems which cannot be handled by algo rithms, and if that is the case, to give concrete cases of this kind. Many such investigations were carried out during the last few decades. The undecidability of arithmetic and other mathematical theories was shown, further the unsolvability of the word problem of group theory. Many mathematicians consider these results and the theory on which they are based to be the most characteristic achievements of mathe matics in the first half of the twentieth century. If we grant the legitimacy of the suggested precise replacements of the concept of algorithm and related concepts, then we can say that the mathematicians have shown by strictly mathematical methods that there exist mathematical problems which cannot be dealt with by the methods of calculating mathematics. In view of the important role which mathematics plays today in our conception of the world this fact is of great philosophical interest. Post speaks of a natural law about the "limitations of the mathematicizing power of Homo Sapiens". Here we also find a starting point for the discussion of the question, what the actual creative activity of the mathematician consists in. In this book we shall give an introduction to the theory of algorithms.

Enumerability, Decidability, Computability

Author : Hans Hermes
Publisher : Springer
ISBN 13 : 3662116863
Total Pages : 255 pages
Book Rating : 4.6/5 (621 download)

DOWNLOAD NOW!

Book Synopsis Enumerability, Decidability, Computability by : Hans Hermes

Download or read book Enumerability, Decidability, Computability written by Hans Hermes and published by Springer. This book was released on 2013-03-14 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: The task of developing algorithms to solve problems has always been considered by mathematicians to be an especially interesting and im portant one. Normally an algorithm is applicable only to a narrowly limited group of problems. Such is for instance the Euclidean algorithm, which determines the greatest common divisor of two numbers, or the well-known procedure which is used to obtain the square root of a natural number in decimal notation. The more important these special algorithms are, all the more desirable it seems to have algorithms of a greater range of applicability at one's disposal. Throughout the centuries, attempts to provide algorithms applicable as widely as possible were rather unsuc cessful. It was only in the second half of the last century that the first appreciable advance took place. Namely, an important group of the inferences of the logic of predicates was given in the form of a calculus. (Here the Boolean algebra played an essential pioneer role. ) One could now perhaps have conjectured that all mathematical problems are solvable by algorithms. However, well-known, yet unsolved problems (problems like the word problem of group theory or Hilbert's tenth problem, which considers the question of solvability of Diophantine equations) were warnings to be careful. Nevertheless, the impulse had been given to search for the essence of algorithms. Leibniz already had inquired into this problem, but without success.

Enumerability. Decidability. Computability

Author : Hans Hermes
Publisher :
ISBN 13 :
Total Pages : 245 pages
Book Rating : 4.:/5 (7 download)

DOWNLOAD NOW!

Book Synopsis Enumerability. Decidability. Computability by : Hans Hermes

Download or read book Enumerability. Decidability. Computability written by Hans Hermes and published by . This book was released on 1969 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Enumerability, Decidability, Computability

Author : Hans Hermes
Publisher :
ISBN 13 : 9783662116876
Total Pages : 256 pages
Book Rating : 4.1/5 (168 download)

DOWNLOAD NOW!

Book Synopsis Enumerability, Decidability, Computability by : Hans Hermes

Download or read book Enumerability, Decidability, Computability written by Hans Hermes and published by . This book was released on 2014-01-15 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computability Theory

Author : Neil D. Jones
Publisher : Academic Press
ISBN 13 : 1483218481
Total Pages : 169 pages
Book Rating : 4.4/5 (832 download)

DOWNLOAD NOW!

Book Synopsis Computability Theory by : Neil D. Jones

Download or read book Computability Theory written by Neil D. Jones and published by Academic Press. This book was released on 2014-06-20 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability Theory: An Introduction provides information pertinent to the major concepts, constructions, and theorems of the elementary theory of computability of recursive functions. This book provides mathematical evidence for the validity of the Church–Turing thesis. Organized into six chapters, this book begins with an overview of the concept of effective process so that a clear understanding of the effective computability of partial and total functions is obtained. This text then introduces a formal development of the equivalence of Turing machine computability, enumerability, and decidability with other formulations. Other chapters consider the formulas of the predicate calculus, systems of recursion equations, and Post's production systems. This book discusses as well the fundamental properties of the partial recursive functions and the recursively enumerable sets. The final chapter deals with different formulations of the basic ideas of computability that are equivalent to Turing-computability. This book is a valuable resource for undergraduate or graduate students.

Computability and Decidability

Author : J. Loeckx
Publisher : Springer Science & Business Media
ISBN 13 : 3642806899
Total Pages : 84 pages
Book Rating : 4.6/5 (428 download)

DOWNLOAD NOW!

Book Synopsis Computability and Decidability by : J. Loeckx

Download or read book Computability and Decidability written by J. Loeckx and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present Lecture Notes evolved from a course given at the Technische Hogeschool Eindhoven and later at the Technische Hogeschool Twente. They are intended for computer science students; more specifically, their goal is to introduce the notions of computability and decidability, and to prepare for the study of automata theory, formal language theory and the theory of computing. Except for a general mathematical background no preliminary knowledge is presupposed, but some experience in programming may be helpful. While classical treatises on computability and decidability are oriented towards the foundation of mathematics or mathematical logic, the present notes try to relate the subject to computer science. Therefore, the expose is based on the use of strings rather than on that of natural numbers; the notations are similar to those in use in automata theory; in addition, according to a common usage in formal language theory, most of the proofs of computability are reduced to the semi-formal description of a procedure the constructivity of which is apparent to anybody having some programming experience. Notwithstanding these facts the subject is treated with mathematical rigor; a great number of informal comments are inserted in order to allow a good intuitive understanding. I am indebted to all those who drew my attention to some errors and ambiguities in a preliminary version of these Notes. I want also to thank Miss L.A. Krukerink for her diligence in typing the manuscript.

What Can Be Computed?

Author : John MacCormick
Publisher : Princeton University Press
ISBN 13 : 0691170665
Total Pages : 404 pages
Book Rating : 4.6/5 (911 download)

DOWNLOAD NOW!

Book Synopsis What Can Be Computed? by : John MacCormick

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

Computability, Complexity, and Languages

Author : Martin Davis
Publisher : Academic Press
ISBN 13 : 0122063821
Total Pages : 631 pages
Book Rating : 4.1/5 (22 download)

DOWNLOAD NOW!

Book Synopsis Computability, Complexity, and Languages by : Martin Davis

Download or read book Computability, Complexity, and Languages written by Martin Davis and published by Academic Press. This book was released on 1994-02-03 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text covers the key areas of computer science, including recursive function theory, formal languages, and automata. Additions to the second edition include: extended exercise sets, which vary in difficulty; expanded section on recursion theory; new chapters on program verification and logic programming; updated references and examples throughout.

Cornerstones of Undecidability

Author : Grzegorz Rozenberg
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!

Book Synopsis Cornerstones of Undecidability by : Grzegorz Rozenberg

Download or read book Cornerstones of Undecidability written by Grzegorz Rozenberg and published by . This book was released on 1994 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents one of the most intellectually challenging aspects of computer related mathematics/logic in a way which should make it accessible to a wider audience. The authors look at different types of reduction to show undecidability, but do so using the novel approach of conversation between three famous mathematicians - sometimes using their own words and sometimes in an adapted form. The authors are of international repute and they provide a modern and authoritative treatment of undecidability with special emphasis on rigorous proofs. Numerous worked examples are included.

Mathematical Logic

Author : H.-D. Ebbinghaus
Publisher : Springer Science & Business Media
ISBN 13 : 1475723555
Total Pages : 290 pages
Book Rating : 4.4/5 (757 download)

DOWNLOAD NOW!

Book Synopsis Mathematical Logic by : H.-D. Ebbinghaus

Download or read book Mathematical Logic written by H.-D. Ebbinghaus and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

Computable Functions

Author : Nikolai Konstantinovich Vereshchagin
Publisher : American Mathematical Soc.
ISBN 13 : 0821827324
Total Pages : 178 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Computable Functions by : Nikolai Konstantinovich Vereshchagin

Download or read book Computable Functions written by Nikolai Konstantinovich Vereshchagin and published by American Mathematical Soc.. This book was released on 2003 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the lectures for undergraduates at Moscow State University, this book presents a lively and concise introduction to the central facts and basic notions of the general theory of computation. It begins with the definition of a computable function and an algorithm, and discusses decidability, enumerability, universal functions, numberings and their properties, the fixed point theorem, arithmetical hierarchy, oracle computations, and degrees.

Computability and Logic

Author : George S. Boolos
Publisher : Cambridge University Press
ISBN 13 : 0521877520
Total Pages : 365 pages
Book Rating : 4.5/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Computability and Logic by : George S. Boolos

Download or read book Computability and Logic written by George S. Boolos and published by Cambridge University Press. This book was released on 2007-09-17 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fifth edition of 'Computability and Logic' covers not just the staple topics of an intermediate logic course such as Godel's incompleteness theorems, but also optional topics that include Turing's theory of computability and Ramsey's theorem.

Computability and Complexity

Author : Neil D. Jones
Publisher : MIT Press
ISBN 13 : 9780262100649
Total Pages : 494 pages
Book Rating : 4.1/5 (6 download)

DOWNLOAD NOW!

Book Synopsis Computability and Complexity by : Neil D. Jones

Download or read book Computability and Complexity written by Neil D. Jones and published by MIT Press. This book was released on 1997 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability and complexity theory should be of central concern to practitioners as well as theorists. Unfortunately, however, the field is known for its impenetrability. Neil Jones's goal as an educator and author is to build a bridge between computability and complexity theory and other areas of computer science, especially programming. In a shift away from the Turing machine- and G�del number-oriented classical approaches, Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists and more applicable to practical programming problems. According to Jones, the fields of computability and complexity theory, as well as programming languages and semantics, have a great deal to offer each other. Computability and complexity theory have a breadth, depth, and generality not often seen in programming languages. The programming language community, meanwhile, has a firm grasp of algorithm design, presentation, and implementation. In addition, programming languages sometimes provide computational models that are more realistic in certain crucial aspects than traditional models. New results in the book include a proof that constant time factors do matter for its programming-oriented model of computation. (In contrast, Turing machines have a counterintuitive "constant speedup" property: that almost any program can be made to run faster, by any amount. Its proof involves techniques irrelevant to practice.) Further results include simple characterizations in programming terms of the central complexity classes PTIME and LOGSPACE, and a new approach to complete problems for NLOGSPACE, PTIME, NPTIME, and PSPACE, uniformly based on Boolean programs. Foundations of Computing series

Turing Computability

Author : Robert I. Soare
Publisher : Springer
ISBN 13 : 3642319335
Total Pages : 289 pages
Book Rating : 4.6/5 (423 download)

DOWNLOAD NOW!

Book Synopsis Turing Computability by : Robert I. Soare

Download or read book Turing Computability written by Robert I. Soare and published by Springer. This book was released on 2016-06-20 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Turing's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic. The author presents the subject as an art to be practiced, and an art in the aesthetic sense of inherent beauty which all mathematicians recognize in their subject. Part I gives a thorough development of the foundations of computability, from the definition of Turing machines up to finite injury priority arguments. Key topics include relative computability, and computably enumerable sets, those which can be effectively listed but not necessarily effectively decided, such as the theorems of Peano arithmetic. Part II includes the study of computably open and closed sets of reals and basis and nonbasis theorems for effectively closed sets. Part III covers minimal Turing degrees. Part IV is an introduction to games and their use in proving theorems. Finally, Part V offers a short history of computability theory. The author has honed the content over decades according to feedback from students, lecturers, and researchers around the world. Most chapters include exercises, and the material is carefully structured according to importance and difficulty. The book is suitable for advanced undergraduate and graduate students in computer science and mathematics and researchers engaged with computability and mathematical logic.

Logic, Logic, and Logic

Author : George Boolos
Publisher : Harvard University Press
ISBN 13 : 9780674537675
Total Pages : 458 pages
Book Rating : 4.5/5 (376 download)

DOWNLOAD NOW!

Book Synopsis Logic, Logic, and Logic by : George Boolos

Download or read book Logic, Logic, and Logic written by George Boolos and published by Harvard University Press. This book was released on 1998 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.

Lectures on the Philosophy of Mathematics

Author : Joel David Hamkins
Publisher : MIT Press
ISBN 13 : 0262542234
Total Pages : 350 pages
Book Rating : 4.2/5 (625 download)

DOWNLOAD NOW!

Book Synopsis Lectures on the Philosophy of Mathematics by : Joel David Hamkins

Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Mathematics in Computing

Author : Gerard O’Regan
Publisher : Springer Nature
ISBN 13 : 3030342093
Total Pages : 468 pages
Book Rating : 4.0/5 (33 download)

DOWNLOAD NOW!

Book Synopsis Mathematics in Computing by : Gerard O’Regan

Download or read book Mathematics in Computing written by Gerard O’Regan and published by Springer Nature. This book was released on 2020-01-10 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The text spans a broad selection of key topics, ranging from the use of finite field theory to correct code and the role of number theory in cryptography, to the value of graph theory when modelling networks and the importance of formal methods for safety critical systems. This fully updated new edition has been expanded with a more comprehensive treatment of algorithms, logic, automata theory, model checking, software reliability and dependability, algebra, sequences and series, and mathematical induction. Topics and features: includes numerous pedagogical features, such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary; describes the historical contributions of such prominent figures as Leibniz, Babbage, Boole, and von Neumann; introduces the fundamental mathematical concepts of sets, relations and functions, along with the basics of number theory, algebra, algorithms, and matrices; explores arithmetic and geometric sequences and series, mathematical induction and recursion, graph theory, computability and decidability, and automata theory; reviews the core issues of coding theory, language theory, software engineering, and software reliability, as well as formal methods and model checking; covers key topics on logic, from ancient Greek contributions to modern applications in AI, and discusses the nature of mathematical proof and theorem proving; presents a short introduction to probability and statistics, complex numbers and quaternions, and calculus. This engaging and easy-to-understand book will appeal to students of computer science wishing for an overview of the mathematics used in computing, and to mathematicians curious about how their subject is applied in the field of computer science. The book will also capture the interest of the motivated general reader.