The Pillars Of Computation Theory

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The Pillars Of Computation Theory

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Author : Arnold L. Rosenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-27

The Pillars Of Computation Theory written by Arnold L. Rosenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-27 with Computers categories.

The abstract branch of theoretical computer science known as Computation Theory typically appears in undergraduate academic curricula in a form that obscures both the mathematical concepts that are central to the various components of the theory and the relevance of the theory to the typical student. This regrettable situation is due largely to the thematic tension among three main competing principles for organizing the material in the course. This book is motivated by the belief that a deep understanding of, and operational control over, the few "big" mathematical ideas that underlie Computation Theory is the best way to enable the typical student to assimilate the "big" ideas of Computation Theory into her daily computational life.

Understanding Computation

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Author : Arnold L. Rosenberg
language : en
Publisher: Springer Nature
Release Date : 2022-09-10

Understanding Computation written by Arnold L. Rosenberg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-10 with Computers categories.

Computation theory is a discipline that uses mathematical concepts and tools to expose the nature of "computation" and to explain a broad range of computational phenomena: Why is it harder to perform some computations than others? Are the differences in difficulty that we observe inherent, or are they artifacts of the way we try to perform the computations? How does one reason about such questions? This unique textbook strives to endow students with conceptual and manipulative tools necessary to make computation theory part of their professional lives. The work achieves this goal by means of three stratagems that set its approach apart from most other texts on the subject. For starters, it develops the necessary mathematical concepts and tools from the concepts' simplest instances, thereby helping students gain operational control over the required mathematics. Secondly, it organizes development of theory around four "pillars," enabling students to see computational topics that have the same intellectual origins in physical proximity to one another. Finally, the text illustrates the "big ideas" that computation theory is built upon with applications of these ideas within "practical" domains in mathematics, computer science, computer engineering, and even further afield. Suitable for advanced undergraduate students and beginning graduates, this textbook augments the "classical" models that traditionally support courses on computation theory with novel models inspired by "real, modern" computational topics,such as crowd-sourced computing, mobile computing, robotic path planning, and volunteer computing. Arnold L. Rosenberg is Distinguished Univ. Professor Emeritus at University of Massachusetts, Amherst, USA. Lenwood S. Heath is Professor at Virgina Tech, Blacksburg, USA.

Elements Of Computation Theory

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Author : Arindama Singh
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-30

Elements Of Computation Theory written by Arindama Singh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-30 with Computers categories.

The foundation of computer science is built upon the following questions: What is an algorithm? What can be computed and what cannot be computed? What does it mean for a function to be computable? How does computational power depend upon programming constructs? Which algorithms can be considered feasible? For more than 70 years, computer scientists are searching for answers to such qu- tions. Their ingenious techniques used in answering these questions form the theory of computation. Theory of computation deals with the most fundamental ideas of computer s- ence in an abstract but easily understood form. The notions and techniques employed are widely spread across various topics and are found in almost every branch of c- puter science. It has thus become more than a necessity to revisit the foundation, learn the techniques, and apply them with con?dence. Overview and Goals This book is about this solid, beautiful, and pervasive foundation of computer s- ence. It introduces the fundamental notions, models, techniques, and results that form the basic paradigms of computing. It gives an introduction to the concepts and mathematics that computer scientists of our day use to model, to argue about, and to predict the behavior of algorithms and computation. The topics chosen here have shown remarkable persistence over the years and are very much in current use.

Fundamentals Of Computation Theory

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Author : R. V. Freĭvald
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-08-03

Fundamentals Of Computation Theory written by R. V. Freĭvald and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-03 with Computers categories.

This book constitutes the refereed proceedings of the 13th International Symposium Fundamentals of Computation Theory, FCT 2001, as well as of the International Workshop on Efficient Algorithms, WEA 2001, held in Riga, Latvia, in August 2001. The 28 revised full FCT papers and 15 short papers presented together with six invited contributions and 8 revised full WEA papers as well as three invited WEA contributions have been carefully reviewed and selected. Among the topics addressed are a broad variety of topics from theoretical computer science, algorithmics and programming theory. The WEA papers deal with graph and network algorithms, flow and routing problems, scheduling and approximation algorithms, etc.

Concise Guide To Computation Theory

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Author : Akira Maruoka
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-29

Concise Guide To Computation Theory written by Akira Maruoka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-29 with Computers categories.

This textbook presents a thorough foundation to the theory of computation. Combining intuitive descriptions and illustrations with rigorous arguments and detailed proofs for key topics, the logically structured discussion guides the reader through the core concepts of automata and languages, computability, and complexity of computation. Topics and features: presents a detailed introduction to the theory of computation, complete with concise explanations of the mathematical prerequisites; provides end-of-chapter problems with solutions, in addition to chapter-opening summaries and numerous examples and definitions throughout the text; draws upon the author’s extensive teaching experience and broad research interests; discusses finite automata, context-free languages, and pushdown automata; examines the concept, universality and limitations of the Turing machine; investigates computational complexity based on Turing machines and Boolean circuits, as well as the notion of NP-completeness.

Computability And Complexity Theory

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Author : Steven Homer
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-09

Computability And Complexity Theory written by Steven Homer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-09 with Computers categories.

This revised and extensively expanded edition of Computability and Complexity Theory comprises essential materials that are core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations. Subsequent chapters move from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Dedicated chapters on undecidability, NP-completeness, and relative computability focus on the limitations of computability and the distinctions between feasible and intractable. Substantial new content in this edition includes: a chapter on nonuniformity studying Boolean circuits, advice classes and the important result of Karp─Lipton. a chapter studying properties of the fundamental probabilistic complexity classes a study of the alternating Turing machine and uniform circuit classes. an introduction of counting classes, proving the famous results of Valiant and Vazirani and of Toda a thorough treatment of the proof that IP is identical to PSPACE With its accessibility and well-devised organization, this text/reference is an excellent resource and guide for those looking to develop a solid grounding in the theory of computing. Beginning graduates, advanced undergraduates, and professionals involved in theoretical computer science, complexity theory, and computability will find the book an essential and practical learning tool. Topics and features: Concise, focused materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes Contains information that otherwise exists only in research literature and presents it in a unified, simplified manner Provides key mathematical background information, including sections on logic and number theory and algebra Supported by numerous exercises and supplementary problems for reinforcement and self-study purposes

Fundamentals Of Computation Theory

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Author : Ralf Klasing
language : en
Publisher: Springer
Release Date : 2017-08-28

Fundamentals Of Computation Theory written by Ralf Klasing and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-28 with Computers categories.

This book constitutes the refereed proceedings of the 21st International Symposium on Fundamentals of Computation Theory, FCT 2017, held in Bordeaux, France, in September 2017. The 29 revised full papers and 5 invited papers presented were carefully reviewed and selected from 99 submissions. The papers cover topics of all aspects of theoretical computer science, in particular algorithms, complexity, formal and logical methods.

Computability

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Author : George Tourlakis
language : en
Publisher: Springer Nature
Release Date : 2022-08-02

Computability written by George Tourlakis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-02 with Computers categories.

This survey of computability theory offers the techniques and tools that computer scientists (as well as mathematicians and philosophers studying the mathematical foundations of computing) need to mathematically analyze computational processes and investigate the theoretical limitations of computing. Beginning with an introduction to the mathematisation of “mechanical process” using URM programs, this textbook explains basic theory such as primitive recursive functions and predicates and sequence-coding, partial recursive functions and predicates, and loop programs. Advanced chapters cover the Ackerman function, Tarski’s theorem on the non-representability of truth, Goedel’s incompleteness and Rosser’s incompleteness theorems, two short proofs of the incompleteness theorem that are based on Lob's deliverability conditions, Church’s thesis, the second recursion theorem and applications, a provably recursive universal function for the primitive recursive functions, Oracle computations and various classes of computable functionals, the Arithmetical hierarchy, Turing reducibility and Turing degrees and the priority method, a thorough exposition of various versions of the first recursive theorem, Blum’s complexity, Hierarchies of primitive recursive functions, and a machine-independent characterisation of Cobham's feasibly computable functions.

Understand Mathematics Understand Computing

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Author : Arnold L. Rosenberg
language : en
Publisher: Springer Nature
Release Date : 2020-12-05

Understand Mathematics Understand Computing written by Arnold L. Rosenberg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-05 with Computers categories.

In this book the authors aim to endow the reader with an operational, conceptual, and methodological understanding of the discrete mathematics that can be used to study, understand, and perform computing. They want the reader to understand the elements of computing, rather than just know them. The basic topics are presented in a way that encourages readers to develop their personal way of thinking about mathematics. Many topics are developed at several levels, in a single voice, with sample applications from within the world of computing. Extensive historical and cultural asides emphasize the human side of mathematics and mathematicians. By means of lessons and exercises on “doing” mathematics, the book prepares interested readers to develop new concepts and invent new techniques and technologies that will enhance all aspects of computing. The book will be of value to students, scientists, and engineers engaged in the design and use of computing systems, and to scholars and practitioners beyond these technical fields who want to learn and apply novel computational ideas.

Topics In Parallel And Distributed Computing

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Author : Sushil K Prasad
language : en
Publisher: Morgan Kaufmann
Release Date : 2015-09-16

Topics In Parallel And Distributed Computing written by Sushil K Prasad and has been published by Morgan Kaufmann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-16 with Computers categories.

Topics in Parallel and Distributed Computing provides resources and guidance for those learning PDC as well as those teaching students new to the discipline. The pervasiveness of computing devices containing multicore CPUs and GPUs, including home and office PCs, laptops, and mobile devices, is making even common users dependent on parallel processing. Certainly, it is no longer sufficient for even basic programmers to acquire only the traditional sequential programming skills. The preceding trends point to the need for imparting a broad-based skill set in PDC technology. However, the rapid changes in computing hardware platforms and devices, languages, supporting programming environments, and research advances, poses a challenge both for newcomers and seasoned computer scientists. This edited collection has been developed over the past several years in conjunction with the IEEE technical committee on parallel processing (TCPP), which held several workshops and discussions on learning parallel computing and integrating parallel concepts into courses throughout computer science curricula. Contributed and developed by the leading minds in parallel computing research and instruction Provides resources and guidance for those learning PDC as well as those teaching students new to the discipline Succinctly addresses a range of parallel and distributed computing topics Pedagogically designed to ensure understanding by experienced engineers and newcomers Developed over the past several years in conjunction with the IEEE technical committee on parallel processing (TCPP), which held several workshops and discussions on learning parallel computing and integrating parallel concepts