Proofs And Algorithms
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Proofs And Algorithms
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Author : Gilles Dowek
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-11
Proofs And Algorithms written by Gilles Dowek 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 2011-01-11 with Computers categories.
Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation. Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself. Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.
Computer Algorithms
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Author : MEHTA, SHASHANK K.
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2023-04-10
Computer Algorithms written by MEHTA, SHASHANK K. and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-10 with Computers categories.
The book is self-contained and includes the desired mathematical background. The book covers most of the data structures and classical graphs algorithms, string algorithms, matroid algorithms, linear algebra algorithms, flow and circulation algorithms, linear programming solvers, and integer algorithms. It covers several topics which are rarely covered in the existing textbooks. Pseudocode is provided for every algorithm. Proof of correctness and the complexity analysis is given for every algorithm. Examples are also provided to help explain several algorithms. The book is designed for an introductory as well as an advance course in the design and analysis of algorithms. It is intended for undergraduate as well as postgraduate students of computer science and engineering. Some of the topics covered in the book are as follows. i) String homomorphism and isomorphism ii) Detailed proof of graph matching algorithm including augmenting path computation iii) Gallai Edmonds decomposition algorithm iv) Matroid Intersection algorithm Klein’s Cycle Cancellation algorithm and Goldberg-Karp’s Minimum Cost Circulation algorithm v) Lower-triangular Upper-triangular decomposition of a matrix using Gaussian Elimination Interior Point method for Linear Programs using Primal-Dual technique vi) Minimum weight Graph Matching algorithm vii) Schonhage-Strassen’s algorithm for integer multiplication and Agarwal-Kayal-Saxena’s algorithm for primality testing
Computer Arithmetic And Formal Proofs
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Author : Sylvie Boldo
language : en
Publisher: Elsevier
Release Date : 2017-11-17
Computer Arithmetic And Formal Proofs written by Sylvie Boldo and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-17 with Computers categories.
Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs. This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation. Describes the notions of specification and weakest precondition computation and their practical use Shows how to tackle algorithms that extend beyond the realm of simple floating-point arithmetic Includes real analysis and a case study about numerical analysis
Semialgebraic Proofs And Efficient Algorithm Design
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Author : NOAH FLEMING;PRAVESH KOTHARI;TONIANN PITASSI.
language : en
Publisher:
Release Date : 2019
Semialgebraic Proofs And Efficient Algorithm Design written by NOAH FLEMING;PRAVESH KOTHARI;TONIANN PITASSI. and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Algorithms categories.
The book provides the advanced reader with a deep insight into the exciting line of research, namely, proof that a solution exists has enabled an algorithm to find that solution itself with applications in many areas of computer science. It will inspire readers in deploying the techniques in their own further research.
Graph Theory
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Author : Karin R Saoub
language : en
Publisher: CRC Press
Release Date : 2021-03-17
Graph Theory written by Karin R Saoub and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-17 with Mathematics categories.
Graph Theory: An Introduction to Proofs, Algorithms, and Applications Graph theory is the study of interactions, conflicts, and connections. The relationship between collections of discrete objects can inform us about the overall network in which they reside, and graph theory can provide an avenue for analysis. This text, for the first undergraduate course, will explore major topics in graph theory from both a theoretical and applied viewpoint. Topics will progress from understanding basic terminology, to addressing computational questions, and finally ending with broad theoretical results. Examples and exercises will guide the reader through this progression, with particular care in strengthening proof techniques and written mathematical explanations. Current applications and exploratory exercises are provided to further the reader’s mathematical reasoning and understanding of the relevance of graph theory to the modern world. Features The first chapter introduces graph terminology, mathematical modeling using graphs, and a review of proof techniques featured throughout the book The second chapter investigates three major route problems: eulerian circuits, hamiltonian cycles, and shortest paths. The third chapter focuses entirely on trees – terminology, applications, and theory. Four additional chapters focus around a major graph concept: connectivity, matching, coloring, and planarity. Each chapter brings in a modern application or approach. Hints and Solutions to selected exercises provided at the back of the book. Author Karin R. Saoub is an Associate Professor of Mathematics at Roanoke College in Salem, Virginia. She earned her PhD in mathematics from Arizona State University and BA from Wellesley College. Her research focuses on graph coloring and on-line algorithms applied to tolerance graphs. She is also the author of A Tour Through Graph Theory, published by CRC Press.
Modern Cryptography Probabilistic Proofs And Pseudorandomness
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Author : Oded Goldreich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Modern Cryptography Probabilistic Proofs And Pseudorandomness written by Oded Goldreich 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 2013-03-09 with Mathematics categories.
Cryptography is one of the most active areas in current mathematics research and applications. This book focuses on cryptography along with two related areas: the study of probabilistic proof systems, and the theory of computational pseudorandomness. Following a common theme that explores the interplay between randomness and computation, the important notions in each field are covered, as well as novel ideas and insights.
People Problems And Proofs
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Author : Richard J. Lipton
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
People Problems And Proofs written by Richard J. Lipton 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 2013-12-11 with Computers categories.
People, problems, and proofs are the lifeblood of theoretical computer science. Behind the computing devices and applications that have transformed our lives are clever algorithms, and for every worthwhile algorithm there is a problem that it solves and a proof that it works. Before this proof there was an open problem: can one create an efficient algorithm to solve the computational problem? And, finally, behind these questions are the people who are excited about these fundamental issues in our computational world. In this book the authors draw on their outstanding research and teaching experience to showcase some key people and ideas in the domain of theoretical computer science, particularly in computational complexity and algorithms, and related mathematical topics. They show evidence of the considerable scholarship that supports this young field, and they balance an impressive breadth of topics with the depth necessary to reveal the power and the relevance of the work described. Beyond this, the authors discuss the sustained effort of their community, revealing much about the culture of their field. A career in theoretical computer science at the top level is a vocation: the work is hard, and in addition to the obvious requirements such as intellect and training, the vignettes in this book demonstrate the importance of human factors such as personality, instinct, creativity, ambition, tenacity, and luck. The authors' style is characterize d by personal observations, enthusiasm, and humor, and this book will be a source of inspiration and guidance for graduate students and researchers engaged with or planning careers in theoretical computer science.
Lectures On Proof Verification And Approximation Algorithms
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Author : Ernst W. Mayr
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-02-25
Lectures On Proof Verification And Approximation Algorithms written by Ernst W. Mayr 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 1998-02-25 with Computers categories.
This is a self-contained presentation of the enormous recent progress on the interplay between and applications of the theory of probabilistically checkable proofs and approximation algorithms.
Proofs And Algorithms
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Author : Gilles Dowek
language : en
Publisher:
Release Date : 2011-03-30
Proofs And Algorithms written by Gilles Dowek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-30 with categories.
Concepts Of Proof In Mathematics Philosophy And Computer Science
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Author : Dieter Probst
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-07-25
Concepts Of Proof In Mathematics Philosophy And Computer Science written by Dieter Probst and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-25 with Philosophy categories.
A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.