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Author: Ronald V. Book Publisher: Springer Science & Business Media ISBN: 1461397715 Category : Computers Languages : en Pages : 198
Book Description
The subject of this book is string-rewriting systems. It is generally accepted that string-rewriting was first introduced by Axel Thue in the early part of this century. In the 1960's and early 1970's, it received renewed attention due to interest in formal language theory. In the 1980's and 1990's, it has received more interest since it can be viewed as a special case of term rewriting, a subject that has become important in the study of automated deduction. Today, string-rewriting is studied by researchers in theoretical computer science and also by researchers interested in the foundations of artificial intelligence. A sketch of the way that the subject has developed is contained in Chapter 0, and the reader is advised to begin with that chapter. Both authors have been active in the field and have lectured on the subject in several universities. Lecture notes have been produced and dis tributed. This monograph is a result of revising and rewriting those notes. It represents an attempt by the authors to present the concepts that the authors consider to be most fundamental and to gather together the most useful results in such a way that they can be understood and used in studies relating to more general rewriting, to automated deduction, and to algo rithmic problems of algebraic structures. This monograph is written for independent study by researchers in the oretical computer science or in the foundations of artificial intelligence.
Author: Ronald V. Book Publisher: Springer Science & Business Media ISBN: 1461397715 Category : Computers Languages : en Pages : 198
Book Description
The subject of this book is string-rewriting systems. It is generally accepted that string-rewriting was first introduced by Axel Thue in the early part of this century. In the 1960's and early 1970's, it received renewed attention due to interest in formal language theory. In the 1980's and 1990's, it has received more interest since it can be viewed as a special case of term rewriting, a subject that has become important in the study of automated deduction. Today, string-rewriting is studied by researchers in theoretical computer science and also by researchers interested in the foundations of artificial intelligence. A sketch of the way that the subject has developed is contained in Chapter 0, and the reader is advised to begin with that chapter. Both authors have been active in the field and have lectured on the subject in several universities. Lecture notes have been produced and dis tributed. This monograph is a result of revising and rewriting those notes. It represents an attempt by the authors to present the concepts that the authors consider to be most fundamental and to gather together the most useful results in such a way that they can be understood and used in studies relating to more general rewriting, to automated deduction, and to algo rithmic problems of algebraic structures. This monograph is written for independent study by researchers in the oretical computer science or in the foundations of artificial intelligence.
Author: Terese Publisher: Cambridge University Press ISBN: 9780521391153 Category : Computers Languages : en Pages : 926
Book Description
Term rewriting systems developed out of mathematical logic and are an important part of theoretical computer science. They consist of sequences of discrete transformation steps where one term is replaced with another and have applications in many areas, from functional programming to automatic theorem proving and computer algebra. This 2003 book starts at an elementary level with the earlier chapters providing a foundation for the rest of the work. Much of the advanced material appeared here for the first time in book form. Subjects treated include orthogonality, termination, completion, lambda calculus, higher-order rewriting, infinitary rewriting and term graph rewriting. Many exercises are included with selected solutions provided on the web. A comprehensive bibliography makes this book ideal both for teaching and research. A chapter is included presenting applications of term rewriting systems, with many pointers to actual implementations.
Author: Alfons Geser Publisher: ISBN: Category : Languages : en Pages : 18
Book Description
Loops are the most frequent cause of non-termination in string rewriting. In the general case, non-terminating, non-looping string rewriting systems exist, and the uniform termination problem is undecidable. For rewriting with only one string rewriting rule, it is unknown whether non-terminating, non-looping systems exist and whether uniform termination is decidable. If in the one-rule case, non-termination is equivalent to the existence of loops, as McNaughton conjectures, then a decision procedure for the existence of loops also solves the uniform termination problem. As the existence of loops of bounded lengths is decidable, the question is raised how long shortest loops may be. We show that string rewriting rules exist whose shortest loops have superexponential lengths in the size of the rule.
Author: M. R. Sleep Publisher: ISBN: Category : Computers Languages : en Pages : 408
Book Description
A comprehensive study and exposition on the benefits of graph and term rewriting. Contains such theoretical advances as a single pushout categorical model of graph rewriting, a new theory of transfinite term rewriting and an abstract interpretation for term graph rewriting. Includes a discussion of parallelism.
Author: Przemyslaw Prusinkiewicz Publisher: Springer Science & Business Media ISBN: 1461384761 Category : Computers Languages : en Pages : 235
Book Description
Now available in an affordable softcover edition, this classic in Springer's acclaimed Virtual Laboratory series is the first comprehensive account of the computer simulation of plant development. 150 illustrations, one third of them in colour, vividly demonstrate the spectacular results of the algorithms used to model plant shapes and developmental processes. The latest in computer-generated images allow us to look at plants growing, self-replicating, responding to external factors and even mutating, without becoming entangled in the underlying mathematical formulae involved. The authors place particular emphasis on Lindenmayer systems - a notion conceived by one of the authors, Aristid Lindenmayer, and internationally recognised for its exceptional elegance in modelling biological phenomena. Nonetheless, the two authors take great care to present a survey of alternative methods for plant modelling.
Author: Matthias Jantzen Publisher: Springer Science & Business Media ISBN: 364261549X Category : Mathematics Languages : en Pages : 133
Book Description
Replacement systems, such as term rewriting systems, tree manipulat ing systems, and graph grammars, have been used in Computer Science in the context of theorem proving, program optimization, abstract data types, algebraic simplification, and symbolic comput ation. Replacement systems for strings arose about seventy years earlier in the area of combinatory logic and group theory. The most natural and appropriate formalism for dealing with string rewriting is the notion of a semi-Thue system and this monograph treats its central aspects. The reduction relation is here defined firstly by the direction of the rules and secondly by some metric that yields efficient algorithms. These systems are general enough to discuss the basic notions of arbitrary replacement systems, such as termination, confluence, and the Church-Rosser property in its original meaning. Confluent semi-Thue systems in which each and every derivation consists of finitely many steps only are called complete; they guarantee the existence of unique normal forms as canonical representatives of the Thue congruence classes. Each such system can be considered a nondeterministic algorithm for the word problem which works correctly without backtracking. This is often conceptually simpler and more elegant than an ad hoc construction. In many cases a replace ment system can be altered to a complete system by the Knuth-Bendix completion method.
Author: Manuel Clavel Publisher: Springer ISBN: 3540719997 Category : Computers Languages : en Pages : 799
Book Description
Maude is a language and system based on rewriting logic. In this comprehensive account, you’ll discover how Maude and its formal tool environment can be used in three mutually reinforcing ways: as a declarative programming language, as an executable formal specification language, and as a formal verification system. Examples used throughout the book illustrate key concepts, features, and the many practical uses of Maude.
Author: Jeffrey C. Lagarias Publisher: American Mathematical Society ISBN: 1470472899 Category : Mathematics Languages : en Pages : 360
Book Description
The $3x+1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then “multiply by three and add one”, while if it is even then “divide by two”. The $3x+1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem, which verify its truth for $x < 5.4 cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000.
Author: Mark V. Sapir Publisher: Springer ISBN: 3319080318 Category : Mathematics Languages : en Pages : 369
Book Description
Combinatorial Algebra: Syntax and Semantics provides comprehensive account of many areas of combinatorial algebra. It contains self-contained proofs of more than 20 fundamental results, both classical and modern. This includes Golod–Shafarevich and Olshanskii's solutions of Burnside problems, Shirshov's solution of Kurosh's problem for PI rings, Belov's solution of Specht's problem for varieties of rings, Grigorchuk's solution of Milnor's problem, Bass–Guivarc'h theorem about growth of nilpotent groups, Kleiman's solution of Hanna Neumann's problem for varieties of groups, Adian's solution of von Neumann-Day's problem, Trahtman's solution of the road coloring problem of Adler, Goodwyn and Weiss. The book emphasize several ``universal" tools, such as trees, subshifts, uniformly recurrent words, diagrams and automata. With over 350 exercises at various levels of difficulty and with hints for the more difficult problems, this book can be used as a textbook, and aims to reach a wide and diversified audience. No prerequisites beyond standard courses in linear and abstract algebra are required. The broad appeal of this textbook extends to a variety of student levels: from advanced high-schoolers to undergraduates and graduate students, including those in search of a Ph.D. thesis who will benefit from the “Further reading and open problems” sections at the end of Chapters 2 –5. The book can also be used for self-study, engaging those beyond t he classroom setting: researchers, instructors, students, virtually anyone who wishes to learn and better understand this important area of mathematics.
Author: Stan Wagon Publisher: Springer Science & Business Media ISBN: 9780387986845 Category : Computers Languages : en Pages : 624
Book Description
"Mathematica in Action, 2nd Edition," is designed both as a guide to the extraordinary capabilities of Mathematica as well as a detailed tour of modern mathematics by one of its leading expositors, Stan Wagon. Ideal for teachers, researchers, mathematica enthusiasts. This second edition of the highly sucessful W.H. Freeman version includes an 8 page full color insert and 50% new material all organized around Elementary Topics, Intermediate Applications, and Advanced Projects. In addition, the book uses Mathematica 3.0 throughtout. Mathematica 3.0 notebooks with all the programs and examples discussed in the book are available on the TELOS web site (www.telospub.com). These notebooks contain materials suitable for DOS, Windows, Macintosh and Unix computers. Stan Wagon is well-known in the mathematics (and Mathematica) community as Associate Editor of the "American Mathematical Monthly," a columnist for the "Mathematical Intelligencer" and "Mathematica in Education and Research," author of "The Banach-Tarski Paradox" and "Unsolved Problems in Elementary Geometry and Number Theory (with Victor Klee), as well as winner of the 1987 Lester R. Ford Award for Expository Writing.
Author: Ronald V. Book
Author: Ronald V. Book
Author: Terese
Author: Alfons Geser
Author: M. R. Sleep
Author: Przemyslaw Prusinkiewicz
Author: Matthias Jantzen
Author: Manuel Clavel
Author: Jeffrey C. Lagarias
Author: Mark V. Sapir
Author: Stan Wagon