Logic Foundations The P Vs Np Problem And Information Theoretic Perspectives
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Logic Foundations The P Vs Np Problem And Information Theoretic Perspectives
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Author : Lucien Sina
language : en
Publisher: BoD – Books on Demand
Release Date : 2025-07-17
Logic Foundations The P Vs Np Problem And Information Theoretic Perspectives written by Lucien Sina and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-17 with Mathematics categories.
This groundbreaking textbook presents a new approach to the study of logic by combining classical foundations with modern information-theoretic perspectives. Following a detailed introduction, it offers an information-theoretic formalization of logic. Subsequently, well-known but still unsolved problems, such as the P versus NP problem, are addressed using the provided tools. An optimization algorithm for the target requirements of logical problem-solving-regarding computability, expressiveness, and consistency-is presented, and finally, a few applications in other fields are showcased. The book offers students and researchers a comprehensive journey through the fundamental principles of logic while introducing innovative concepts at the intersection of logic, information theory, and computational complexity. Key features include: -Solid foundations in classical logic, including propositional and predicate logic, validity, and formal inference. -Novel integration of Shannon's information theory with traditional logical concepts. -Exploration of new approaches to axiomatization and formalization in light of Gödel's incompleteness results. -In-depth analysis of the P versus NP problem with information-theoretic and optimization approaches. -Clear explanations and examples suitable for beginners and beyond. -Applications in mathematics, computer science, and related fields.
Algorithms And Data Structures
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Author : Lucien Sina
language : en
Publisher: BoD – Books on Demand
Release Date : 2025-07-09
Algorithms And Data Structures written by Lucien Sina and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-09 with Computers categories.
Master the fundamental principles that govern modern computer science. This comprehensive guide provides a step-by-step approach to designing, analyzing, and implementing efficient algorithms. In it you will discover: -Clear explanations of key algorithms and data structures. -Practical techniques for optimizing runtime and memory usage. -Practical examples and exercises to reinforce your understanding. -A solid foundation for tackling complex programming tasks. -Perfect for students, programmers, and computer scientists who want to improve their problem-solving skills and create powerful applications.
Logic Foundations The P Vs Np Problem And Information Theoretic Perspectives
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Author : Lucien Sina
language : en
Publisher:
Release Date : 2024
Logic Foundations The P Vs Np Problem And Information Theoretic Perspectives written by Lucien Sina and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with categories.
Logical Foundations Of Mathematics And Computational Complexity
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Author : Pavel Pudlák
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-22
Logical Foundations Of Mathematics And Computational Complexity written by Pavel Pudlák 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 2013-04-22 with Mathematics categories.
The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.
Logic And Complexity
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Author : Richard Lassaigne
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Logic And Complexity written by Richard Lassaigne 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 2012-12-06 with Computers categories.
Logic and Complexity looks at basic logic as it is used in Computer Science, and provides students with a logical approach to Complexity theory. With plenty of exercises, this book presents classical notions of mathematical logic, such as decidability, completeness and incompleteness, as well as new ideas brought by complexity theory such as NP-completeness, randomness and approximations, providing a better understanding for efficient algorithmic solutions to problems. Divided into three parts, it covers: - Model Theory and Recursive Functions - introducing the basic model theory of propositional, 1st order, inductive definitions and 2nd order logic. Recursive functions, Turing computability and decidability are also examined. - Descriptive Complexity - looking at the relationship between definitions of problems, queries, properties of programs and their computational complexity. - Approximation - explaining how some optimization problems and counting problems can be approximated according to their logical form. Logic is important in Computer Science, particularly for verification problems and database query languages such as SQL. Students and researchers in this field will find this book of great interest.
P Np And Np Completeness
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Author : Oded Goldreich
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-16
P Np And Np Completeness written by Oded Goldreich and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-16 with Computers categories.
The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not discovering proofs is harder than verifying their correctness. It is widely believed that the answer to these equivalent formulations is positive, and this is captured by saying that P is different from NP. Although the P versus NP Question remains unresolved, the theory of NP-completeness offers evidence for the intractability of specific problems in NP by showing that they are universal for the entire class. Amazingly enough, NP-complete problems exist, and furthermore hundreds of natural computational problems arising in many different areas of mathematics and science are NP-complete.
Computational Complexity A Quantitative Perspective
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Author : Marius Zimand
language : en
Publisher: Elsevier
Release Date : 2004-07-07
Computational Complexity A Quantitative Perspective written by Marius Zimand and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-07 with Computers categories.
There has been a common perception that computational complexity is a theory of "bad news" because its most typical results assert that various real-world and innocent-looking tasks are infeasible. In fact, "bad news" is a relative term, and, indeed, in some situations (e.g., in cryptography), we want an adversary to not be able to perform a certain task. However, a "bad news" result does not automatically become useful in such a scenario. For this to happen, its hardness features have to be quantitatively evaluated and shown to manifest extensively.The book undertakes a quantitative analysis of some of the major results in complexity that regard either classes of problems or individual concrete problems. The size of some important classes are studied using resource-bounded topological and measure-theoretical tools. In the case of individual problems, the book studies relevant quantitative attributes such as approximation properties or the number of hard inputs at each length.One chapter is dedicated to abstract complexity theory, an older field which, however, deserves attention because it lays out the foundations of complexity. The other chapters, on the other hand, focus on recent and important developments in complexity. The book presents in a fairly detailed manner concepts that have been at the centre of the main research lines in complexity in the last decade or so, such as: average-complexity, quantum computation, hardness amplification, resource-bounded measure, the relation between one-way functions and pseudo-random generators, the relation between hard predicates and pseudo-random generators, extractors, derandomization of bounded-error probabilistic algorithms, probabilistically checkable proofs, non-approximability of optimization problems, and others.The book should appeal to graduate computer science students, and to researchers who have an interest in computer science theory and need a good understanding of computational complexity, e.g., researchers in algorithms, AI, logic, and other disciplines.·Emphasis is on relevant quantitative attributes of important results in complexity.·Coverage is self-contained and accessible to a wide audience.·Large range of important topics including: derandomization techniques, non-approximability of optimization problems, average-case complexity, quantum computation, one-way functions and pseudo-random generators, resource-bounded measure and topology.
The Golden Ticket
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Author : Lance Fortnow
language : en
Publisher: Princeton University Press
Release Date : 2017-02-28
The Golden Ticket written by Lance Fortnow and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-28 with Computers categories.
The computer science problem whose solution could transform life as we know it The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. Lance Fortnow traces the history and development of P-NP, giving examples from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.
Computable Foundations For Economics
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Author : K. Vela Velupillai
language : en
Publisher: Routledge
Release Date : 2012-07-26
Computable Foundations For Economics written by K. Vela Velupillai and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-26 with Business & Economics categories.
Computable Foundations for Economics is a unified collection of essays, some of which are published here for the first time and all of which have been updated for this book, on an approach to economic theory from the point of view of algorithmic mathematics. By algorithmic mathematics the author means computability theory and constructive mathematics. This is in contrast to orthodox mathematical economics and game theory, which are formalised with the mathematics of real analysis, underpinned by what is called the ZFC formalism, i.e., set theory with the axiom of choice. This reliance on ordinary real analysis and the ZFC system makes economic theory in its current mathematical mode completely non-algorithmic, which means it is numerically meaningless. The book provides a systematic attempt to dissect and expose the non-algorithmic content of orthodox mathematical economics and game theory and suggests a reformalization on the basis of a strictly rigorous algorithmic mathematics. This removes the current schizophrenia in mathematical economics and game theory, where theory is entirely divorced from algorithmic applicability – for experimental and computational exercises. The chapters demonstrate the uncomputability and non-constructivity of core areas of general equilibrium theory, game theory and recursive macroeconomics. The book also provides a fresh look at the kind of behavioural economics that lies behind Herbert Simon’s work, and resurrects a role for the noble classical traditions of induction and verification, viewed and formalised, now, algorithmically. It will therefore be of particular interest to postgraduate students and researchers in algorithmic economics, game theory and classical behavioural economics.
Proof Complexity
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Author : Jan Krajíček
language : en
Publisher: Cambridge University Press
Release Date : 2019-03-28
Proof Complexity written by Jan Krajíček and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-28 with Computers categories.
Offers a self-contained work presenting basic ideas, classical results, current state of the art and possible future directions in proof complexity.