Models Of Computation

A Concise Introduction to Computation Models and Computability Theory provides an introduction to the essential concepts in computability, using several models of computation, from the standard Turing Machines and Recursive Functions, to the modern computation models inspired by quantum physics. An in-depth analysis of the basic concepts underlying each model of computation is provided. Divided into two parts, the first highlights the traditional computation models used in the first studies on computability: - Automata and Turing Machines; - Recursive functions and the Lambda-Calculus; - Logic-based computation models. and the second part covers object-oriented and interaction-based models. There is also a chapter on concurrency, and a final chapter on emergent computation models inspired by quantum mechanics. At the end of each chapter there is a discussion on the use of computation models in the design of programming languages.

This text focuses on finite problems and emphasizes concrete models of machines and programming styles. Using problems defined over infinite domains and abstract machine models as models, emphasis is given to concrete problems of the kind found in algorithms textbooks, as well as machine models related to current technology. The book integrates the theme of parallelism throughout the book (for example, circuits are presented as parallel machines) and studies the exchanges between space, time and other resources on a variety of machine models.

This book presents in their basic form the most important models of computation, their basic programming paradigms, and their mathematical descriptions, both concrete and abstract. Each model is accompanied by relevant formal techniques for reasoning on it and for proving some properties. After preliminary chapters that introduce the notions of structure and meaning, semantic methods, inference rules, and logic programming, the authors arrange their chapters into parts on IMP, a simple imperative language; HOFL, a higher-order functional language; concurrent, nondeterministic and interactive models; and probabilistic/stochastic models. The authors have class-tested the book content over many years, and it will be valuable for graduate and advanced undergraduate students of theoretical computer science and distributed systems, and for researchers in this domain. Each chapter of the book concludes with a list of exercises addressing the key techniques introduced, solutions to selected exercises are offered at the end of the book.

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

This book constitutes the refereed proceedings of the Third International Conference on Unconventional Models of Computation, UMC 2002, held in Kobe, Japan in October 2002.The 18 revised full papers presented together with eight invited full papers were carefully reviewed and selected from 36 submissions. All major areas of unconventinal computing models are covered, especially quantum computing, DNA computing, membrane computing, cellular computing, and possibilities to break Turing's barrier. The authors address theoretical aspects, practical implementations, as well as philosophical reflections.

This book contains papers presented at the 2nd International Conference on Unconventional Models of Computation (UMCK'2K), which was held at Solvay Institutes, Brussels, Belgium, in December 2000. Computers as we know them may be getting better and cheaper, and doing more for us, but they are still unable to cope with many tasks of practical interest. Nature, though, has been 'computing' with molecules and cells for billions of years, and these natural processes form the main motivation for the construction of radically new models of computation, the core theme of the papers in this volume. Unconventional Models of Computation, UMCK'2K covers all major areas of unconventional computation, including quantum computing, DNA-based computation, membrane computing and evolutionary algorithms.

The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.