This book constitutes the refereed proceedings of the 10th International Conference on Theory and Applications of Models of Computation, TAMC 2013, held in Hong Kong, China, in May 2013. The 31 revised full papers presented were carefully reviewed and selected from 70 submissions. Bringing together a wide range of researchers with interests in computational theory and applications, the papers address the three main themes of the conference which were computability, complexity, and algorithms and present current research in these fields with aspects to theoretical computer science, algorithmic mathematics, and applications to the physical sciences.
Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s. This was motivated by questions such as: which real numbers and real number functions are computable, and which mathematical tasks in analysis can be solved by algorithmic means? Nowadays this theory has many different facets that embrace topics from computability theory, algorithmic randomness, computational complexity, dynamical systems, fractals, and analog computers, up to logic, descriptive set theory, constructivism, and reverse mathematics. In recent decades computable analysis has invaded many branches of analysis, and researchers have studied computability and complexity questions arising from real and complex analysis, functional analysis, and the theory of differential equations, up to (geometric) measure theory and topology. This handbook represents the first coherent cross-section through most active research topics on the more theoretical side of the field. It contains 11 chapters grouped into parts on computability in analysis; complexity, dynamics, and randomness; and constructivity, logic, and descriptive complexity. All chapters are written by leading experts working at the cutting edge of the respective topic. Researchers and graduate students in the areas of theoretical computer science and mathematical logic will find systematic introductions into many branches of computable analysis, and a wealth of information and references that will help them to navigate the modern research literature in this field.
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
"Intended as an upper-level undergraduate or introductory graduate text in computer science theory," this book lucidly covers the key concepts and theorems of the theory of computation. The presentation is remarkably clear; for example, the "proof idea," which offers the reader an intuitive feel for how the proof was constructed, accompanies many of the theorems and a proof. Introduction to the Theory of Computation covers the usual topics for this type of text plus it features a solid section on complexity theory--including an entire chapter on space complexity. The final chapter introduces more advanced topics, such as the discussion of complexity classes associated with probabilistic algorithms.
Models of Computation and Formal Languages presents a comprehensive and rigorous treatment of the theory of computability. The text takes a novel approach focusing on computational models and is the first book of its kind to feature companion software. Deus Ex Machina, developed by Nicolae Savoiu, comprises software simulations of the various computational models considered and incorporates numerous examples in a user-friendly format. Part I of the text introduces several universal models including Turing machines, Markov algorithms, and register machines. Complexity theory is integrated gradually, starting in Chapter 1. The vector machine model of parallel computation is covered thoroughly both in text and software. Part II develops the Chomsky hierarchy of formal languages and provides both a grammar-theoretic and an automata-theoretic characterization of each language family. Applications to programming languages round out an in-depth theoretical discussion, making this an ideal text for students approaching this subject for the first time. Ancillary sections of several chapters relate classical computability theory to the philosophy of mind, cognitive science, and theoretical linguistics. Ideal for Theory of Computability and Theory of Algorithms courses at the advanced undergraduate or beginning graduate level, Models of Computation and Formal Languages is one of the only texts that... - - Features accompanying software available on the World Wide Web at http: //home.manhattan.edu/ gregory.taylor/thcomp/ Adopts an integrated approach to complexity theory - Offers a solutions manual containing full solutions to several hundred exercises. Most of these solutions are available to students on the World Wide Web at http: //home.manhattan.edu/ gregory.taylor/thcomp - Features examples relating the theory of computation to the probable programming experience of an undergraduate computer science major
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Formal Languages and Computation: Models and Their Applications gives a clear, comprehensive introduction to formal language theory and its applications in computer science. It covers all rudimental topics concerning formal languages and their models, especially grammars and automata, and sketches the basic ideas underlying the theory of computation, including computability, decidability, and computational complexity. Emphasizing the relationship between theory and application, the book describes many real-world applications, including computer science engineering techniques for language processing and their implementation. Covers the theory of formal languages and their models, including all essential concepts and properties Explains how language models underlie language processors Pays a special attention to programming language analyzers, such as scanners and parsers, based on four language models—regular expressions, finite automata, context-free grammars, and pushdown automata Discusses the mathematical notion of a Turing machine as a universally accepted formalization of the intuitive notion of a procedure Reviews the general theory of computation, particularly computability and decidability Considers problem-deciding algorithms in terms of their computational complexity measured according to time and space requirements Points out that some problems are decidable in principle, but they are, in fact, intractable problems for absurdly high computational requirements of the algorithms that decide them In short, this book represents a theoretically oriented treatment of formal languages and their models with a focus on their applications. It introduces all formalisms concerning them with enough rigors to make all results quite clear and valid. Every complicated mathematical passage is preceded by its intuitive explanation so that even the most complex parts of the book are easy to grasp. After studying this book, both student and professional should be able to understand the fundamental theory of formal languages and computation, write language processors, and confidently follow most advanced books on the subject.
Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.
"Constructive Computation in Stochastic Models with Applications: The RG-Factorizations" provides a unified, constructive and algorithmic framework for numerical computation of many practical stochastic systems. It summarizes recent important advances in computational study of stochastic models from several crucial directions, such as stationary computation, transient solution, asymptotic analysis, reward processes, decision processes, sensitivity analysis as well as game theory. Graduate students, researchers and practicing engineers in the field of operations research, management sciences, applied probability, computer networks, manufacturing systems, transportation systems, insurance and finance, risk management and biological sciences will find this book valuable. Dr. Quan-Lin Li is an Associate Professor at the Department of Industrial Engineering of Tsinghua University, China.
