This volume contains nine selected papers presented at the Borgholm conference. They were chosen on the basis of their immediate relevance to the most fundamental aspects of the theory of computation and the newest developments in this area.These papers, which have been extended and refereed, fall into eight categories: 1. Constructive Mathematics in Models of Computation and Programming; 2. Abstract Calculi and Denotational Semantics; 3. Theory of Machines, Computations and Languages; 4. Nondeterminism, Concurrency and Distributed Computing; 5. Abstract Algebras, Logics and Combinatorics in Computation Theory; 6. General Computability and Decidability; 7. Computational and Arithmetic Complexity; 8. Analysis of Algorithms and Feasible Computing.

Learn the skills and acquire the intuition to assess the theoretical limitations of computer programming Offering an accessible approach to the topic, Theory of Computation focuses on the metatheory of computing and the theoretical boundaries between what various computational models can do and not do—from the most general model, the URM (Unbounded Register Machines), to the finite automaton. A wealth of programming-like examples and easy-to-follow explanations build the general theory gradually, which guides readers through the modeling and mathematical analysis of computational phenomena and provides insights on what makes things tick and also what restrains the ability of computational processes. Recognizing the importance of acquired practical experience, the book begins with the metatheory of general purpose computer programs, using URMs as a straightforward, technology-independent model of modern high-level programming languages while also exploring the restrictions of the URM language. Once readers gain an understanding of computability theory—including the primitive recursive functions—the author presents automata and languages, covering the regular and context-free languages as well as the machines that recognize these languages. Several advanced topics such as reducibilities, the recursion theorem, complexity theory, and Cook's theorem are also discussed. Features of the book include: A review of basic discrete mathematics, covering logic and induction while omitting specialized combinatorial topics A thorough development of the modeling and mathematical analysis of computational phenomena, providing a solid foundation of un-computability The connection between un-computability and un-provability: Gödel's first incompleteness theorem The book provides numerous examples of specific URMs as well as other programming languages including Loop Programs, FA (Deterministic Finite Automata), NFA (Nondeterministic Finite Automata), and PDA (Pushdown Automata). Exercises at the end of each chapter allow readers to test their comprehension of the presented material, and an extensive bibliography suggests resources for further study. Assuming only a basic understanding of general computer programming and discrete mathematics, Theory of Computation serves as a valuable book for courses on theory of computation at the upper-undergraduate level. The book also serves as an excellent resource for programmers and computing professionals wishing to understand the theoretical limitations of their craft.

The two-volume set LNCS 5072 and 5073 constitutes the refereed proceedings of the International Conference on Computational Science and Its Applications, ICCSA 2008, held in Perugia, Italy, in June/July, 2008. The two volumes contain papers presenting a wealth of original research results in the field of computational science, from foundational issues in computer science and mathematics to advanced applications in virtually all sciences making use of computational techniques. The topics of the fully refereed papers are structured according to the five major conference themes: computational methods, algorithms and scientific applications, high performance technical computing and networks, advanced and emerging applications, geometric modelling, graphics and visualization, as well as information systems and information technologies. Moreover, submissions from more than 20 workshops and technical sessions in the areas, such as embedded systems, geographical analysis, computational geometry, computational geomatics, computer graphics, virtual reality, computer modeling, computer algebra, mobile communications, wireless networks, computational forensics, data storage, information security, web learning, software engineering, computational intelligence, digital security, biometrics, molecular structures, material design, ubiquitous computing, symbolic computations, web systems and intelligence, and e-education contribute to this publication.

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.

These ten detailed and authoritative survey articles on numerical methods for direct and inverse wave propagation problems are written by leading experts. Researchers and practitioners in computational wave propagation, from postgraduate level onwards, will find the breadth and depth of coverage of recent developments a valuable resource. The articles describe a wide range of topics on the application and analysis of methods for time and frequency domain PDE and boundary integral formulations of wave propagation problems. Electromagnetic, seismic and acoustic equations are considered. Recent developments in methods and analysis ranging from finite differences to hp-adaptive finite elements, including high-accuracy and fast methods are described with extensive references.

This book provides a comprehensive introduction to advanced topics in the computational and algorithmic aspects of number theory, focusing on applications in cryptography. Readers will learn to develop fast algorithms, including quantum algorithms, to solve various classic and modern number theoretic problems. Key problems include prime number generation, primality testing, integer factorization, discrete logarithms, elliptic curve arithmetic, conjecture and numerical verification. The author discusses quantum algorithms for solving the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP), and the Elliptic Curve Discrete Logarithm Problem (ECDLP) and for attacking IFP, DLP and ECDLP based cryptographic systems. Chapters also cover various other quantum algorithms for Pell's equation, principal ideal, unit group, class group, Gauss sums, prime counting function, Riemann's hypothesis and the BSD conjecture. Quantum Computational Number Theory is self-contained and intended to be used either as a graduate text in computing, communications and mathematics, or as a basic reference in the related fields. Number theorists, cryptographers and professionals working in quantum computing, cryptography and network security will find this book a valuable asset.

Software Engineer's Reference Book provides the fundamental principles and general approaches, contemporary information, and applications for developing the software of computer systems. The book is comprised of three main parts, an epilogue, and a comprehensive index. The first part covers the theory of computer science and relevant mathematics. Topics under this section include logic, set theory, Turing machines, theory of computation, and computational complexity. Part II is a discussion of software development methods, techniques and technology primarily based around a conventional view of the software life cycle. Topics discussed include methods such as CORE, SSADM, and SREM, and formal methods including VDM and Z. Attention is also given to other technical activities in the life cycle including testing and prototyping. The final part describes the techniques and standards which are relevant in producing particular classes of application. The text will be of great use to software engineers, software project managers, and students of computer science.

Issues in Specialized Chemical and Chemistry Topics: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Magnetic Resonance. The editors have built Issues in Specialized Chemical and Chemistry Topics: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Magnetic Resonance in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Specialized Chemical and Chemistry Topics: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

This Festschrift, dedicated to Frits W. Vaandrager on the occasion of his 60th birthday, contains papers written by many of his closest collaborators. Frits has been a Professor of Informatics for Technical Applications at Radboud University Nijmegen since 1995, where his research focuses on formal methods, concurrency theory, verification, model checking, and automata learning. The volume contains contributions of colleagues, Ph.D. students, and researchers with whom Frits has collaborated and inspired, reflecting a wide spectrum of scientific interests, and demonstrating successful work at the highest levels of both theory and practice.

A gentle introduction to advanced topics such as parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to ‘compute’ solutions to problems, hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment - some experience with Diffpack is required. There are also some chapters covering complete applications, i.e., the way from a model, expressed as systems of PDEs, through to discretization methods, algorithms, software design, verification, and computational examples. Suitable for readers with a background in basic finite element and finite difference methods for partial differential equations.