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This textbook discusses the most fundamental and puzzling questions about the foundations of computing. In 23 lecture-sized chapters it provides an exciting tour through the most important results in the field of computability and time complexity, including the Halting Problem, Rice's Theorem, Kleene's Recursion Theorem, the Church-Turing Thesis, Hierarchy Theorems, and Cook-Levin's Theorem. Each chapter contains classroom-tested material, including examples and exercises. Links between adjacent chapters provide a coherent narrative. Fundamental results are explained lucidly by means of programs written in a simple, high-level imperative programming language, which only requires basic mathematical knowledge. Throughout the book, the impact of the presented results on the entire field of computer science is emphasised. Examples range from program analysis to networking, from database programming to popular games and puzzles. Numerous biographical footnotes about the famous scientists who developed the subject are also included. "Limits of Computation" offers a thorough, yet accessible, introduction to computability and complexity for the computer science student of the 21st century.
Computer Science --- Engineering & Applied Sciences --- Computer software. --- Algorithm Analysis and Problem Complexity. --- Mathematics of Algorithmic Complexity. --- Software, Computer --- Computer systems --- Computer programming. --- Algorithms. --- Algorism --- Algebra --- Arithmetic --- Foundations
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The field of parameterized complexity/multivariate complexity algorithmics is an exciting and vibrant part of theoretical computer science, responding to the vital need for efficient algorithms in modern society. This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Topics and features: Describes many of the standard algorithmic techniques available for establishing parametric tractability Reviews the classical hardness classes Explores the various limitations and relaxations of the methods Showcases the powerful new lower bound techniques Examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach Demonstrates how complexity methods and ideas have evolved over the past 25 years This classroom-tested and easy-to-follow textbook/reference is essential reading for the beginning graduate student and advanced undergraduate student. The book will also serve as an invaluable resource for the general computer scientist and the mathematically-aware scientist seeking tools for their research.
Engineering & Applied Sciences --- Computer Science --- Computer science. --- Algorithms. --- Computer Science. --- Algorithm Analysis and Problem Complexity. --- Mathematics of Algorithmic Complexity. --- Algorism --- Algebra --- Arithmetic --- Informatics --- Science --- Foundations --- Computer software. --- Software, Computer --- Computer systems --- Computer algorithms. --- Computer science --- Mathematics.
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This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.
Mathematics. --- Algorithms. --- Computer mathematics. --- Computational Mathematics and Numerical Analysis. --- Mathematics of Algorithmic Complexity. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Algorism --- Algebra --- Arithmetic --- Math --- Science --- Mathematics --- Foundations --- Numerical analysis --- Data processing. --- Computer science --- Applications of Mathematics.
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This Festschrift is in honor of Ker-I Ko, Professor in the Stony Brook University, USA. Ker-I Ko was one of the founding fathers of computational complexity over real numbers and analysis. He and Harvey Friedman devised a theoretical model for real number computations by extending the computation of Turing machines. He contributed significantly to advancing the theory of structural complexity, especially on polynomial-time isomorphism, instance complexity, and relativization of polynomial-time hierarchy. Ker-I also made many contributions to approximation algorithm theory of combinatorial optimization problems. This volume contains 17 contributions in the area of complexity and approximation. Those articles are authored by researchers over the world, including North America, Europe and Asia. Most of them are co-authors, colleagues, friends, and students of Ker-I Ko.
Algorithms. --- Algorithm Analysis and Problem Complexity. --- Mathematics of Algorithmic Complexity. --- Algorism --- Algebra --- Arithmetic --- Foundations --- Computational complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Mathematics. --- Applications of Mathematics. --- Math --- Science
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The book introduces the concept of “generalized interval valued intuitionistic fuzzy soft sets”. It presents the basic properties of these sets and also, investigates an application of generalized interval valued intuitionistic fuzzy soft sets in decision making with respect to interval of degree of preference. The concept of “interval valued intuitionistic fuzzy soft rough sets” is discussed and interval valued intuitionistic fuzzy soft rough set based multi criteria group decision making scheme is presented, which refines the primary evaluation of the whole expert group and enables us to select the optimal object in a most reliable manner. The book also details concept of interval valued intuitionistic fuzzy sets of type 2. It presents the basic properties of these sets. The book also introduces the concept of “interval valued intuitionistic fuzzy soft topological space (IVIFS topological space)” together with intuitionistic fuzzy soft open sets (IVIFS open sets) and intuitionistic fuzzy soft closed sets (IVIFS closed sets).
Engineering. --- Computational Intelligence. --- Complexity. --- Mathematics of Algorithmic Complexity. --- Physics. --- Ingénierie --- Physique --- Engineering & Applied Sciences --- Computer Science --- Algorithms. --- Computational intelligence. --- Complexity, Computational. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Algorism --- Algebra --- Arithmetic --- Construction --- Industrial arts --- Technology --- Foundations --- Computational complexity. --- Fuzzy sets. --- Sets, Fuzzy --- Fuzzy mathematics --- Set theory
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The present volume contains invited talks of 11th biennial conference on “Emerging Mathematical Methods, Models and Algorithms for Science and Technology”. The main message of the book is that mathematics has a great potential to analyse and understand the challenging problems of nanotechnology, biotechnology, medical science, oil industry and financial technology. The book highlights all the features and main theme discussed in the conference. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world.
Applied Mathematics --- Engineering & Applied Sciences --- Mathematical models --- Models, Mathematical --- Mathematics. --- Algorithms. --- Mathematical models. --- Geometry. --- Mathematical optimization. --- Mathematical Modeling and Industrial Mathematics. --- Mathematics of Algorithmic Complexity. --- Optimization. --- Simulation methods --- Mathematics --- Euclid's Elements --- Algorism --- Algebra --- Arithmetic --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- System analysis --- Foundations
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The main theme of this book is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes the latest advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods, and symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in the context of structure preservation. All the new methods introduced in this book are proven to be highly effective compared with the well-known codes in the scientific literature. This book also addresses challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.
Differential equations. --- Functional differential equations. --- Mathematics. --- Algorithms. --- Complexity, Computational. --- Mathematics of Algorithmic Complexity. --- Complexity. --- Differential equations, Functional --- Differential equations --- Functional equations --- 517.91 Differential equations --- Engineering. --- Construction --- Industrial arts --- Technology --- Computational complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Algorism --- Algebra --- Arithmetic --- Foundations
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This thesis presents an accurate and advanced numerical methodology to remedy difficulties such as direct numerical simulation of magnetohydrodynamic (MHD) flow in computational fluid dynamics (CFD), grid generation processes in tokamak fusion facilities, and the coupling between the surface tension force and Lorentz force in the metallurgical industry. In addition, on the basis of the numerical platform it establishes, it also investigates selected interesting topics, e.g. single bubble motion under the influence of either vertical or horizontal magnetic fields. Furthermore, it confirms the relation between the bubble’s path instability and wake instability, and observes the anisotropic (isotropic) effect of the vertical (horizontal) magnetic field on the vortex structures, which determines the dynamic behavior of the rising bubble. The direct numerical simulation of magnetohydrodynamic (MHD) flows has proven difficult in the field of computational fluid dynamic (CFD) research, because it not only concerns the coupling of the equations governing the electromagnetic field and the fluid motion, but also calls for suitable numerical methods for computing the electromagnetic field. In tokamak fusion facilities, where the MHD effect is significant and the flow domain is complex, the process of grid generation requires considerable time and effort. Moreover, in the metallurgical industry, where multiphase MHD flows are usually encountered, the coupling between the surface tension force and Lorentz force adds to the difficulty of deriving direct numerical simulations.
Magnetohydrodynamics --- Mathematical models. --- Hydraulic engineering. --- Mechanics. --- Engineering Fluid Dynamics. --- Classical Mechanics. --- Mathematics of Algorithmic Complexity. --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Hydraulics --- Shore protection --- Fluid mechanics. --- Algorithms. --- Algorism --- Algebra --- Arithmetic --- Hydromechanics --- Continuum mechanics --- Foundations
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This book highlights relevant studies and applications in the area of robotics, which reflect the latest research, from interdisciplinary theoretical studies and computational algorithm development, to representative applications. It presents chapters on advanced control, such as fuzzy, neural, backstepping, sliding mode, adaptive, predictive, diagnosis and fault tolerant control etc. and addresses topics including cloud robotics, cable-driven robots, two-wheeled robots, mobile robots, swarm robots, hybrid vehicle, and drones. Each chapter employs a uniform structure: background, motivation, quantitative development (equations), case studies/illustration/tutorial (simulations, experiences, curves, tables, etc.), allowing readers to easily tailor the techniques to their own applications.
Vibration. --- Artificial intelligence. --- Control and Systems Theory. --- Robotics and Automation. --- Vibration, Dynamical Systems, Control. --- Complex Systems. --- Mathematics of Algorithmic Complexity. --- Artificial Intelligence. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Cycles --- Mechanics --- Sound
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Michael Holzhauser discusses generalizations of well-known network flow and packing problems by additional or modified side constraints. By exploiting the inherent connection between the two problem classes, the author investigates the complexity and approximability of several novel network flow and packing problems and presents combinatorial solution and approximation algorithms. Contents Fractional Packing and Parametric Search Frameworks Budget-Constrained Minimum Cost Flows: The Continuous Case Budget-Constrained Minimum Cost Flows: The Discrete Case Generalized Processing Networks Convex Generalized Flows Target Groups Researchers and students in the fields of mathematics, computer science, and economics Practitioners in operations research and logistics The Author Dr. Michael Holzhauser studied computer science at the University of Kaiserslautern and is now a research fellow in the Optimization Research Group at the Department of Mathematics of the University of Kaiserslautern.
Numerical methods of optimisation --- Operational research. Game theory --- Discrete mathematics --- Mathematics --- Computer science --- discrete wiskunde --- wiskunde --- algoritmen --- Algorithms. --- Discrete Optimization. --- Mathematics of Algorithmic Complexity. --- Algorism --- Algebra --- Arithmetic --- Foundations --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis
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