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Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.

Author : von Friedrich Haeseler
ISBN : 9783110197969
Genre : Mathematics
File Size : 68.60 MB
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Automatic sequences are sequences which are produced by a finite automaton. Although they are not random they may look as being random. They are complicated, in the sense of not being not ultimately periodic, they may look rather complicated, in the sense that it may not be easy to name the rule by which the sequence is generated, however there exists a rule which generates the sequence. The concept automatic sequences has special applications in algebra, number theory, finite automata and formal languages, combinatorics on words. The text deals with different aspects of automatic sequences, in particular: · a general introduction to automatic sequences · the basic (combinatorial) properties of automatic sequences · the algebraic approach to automatic sequences · geometric objects related to automatic sequences.

This book constitutes the refereed proceedings of the 7th International Conference on Language and Automata Theory and Applications, LATA 2013, held in Bilbao, Spain in April 2013. The 45 revised full papers presented together with 5 invited talks were carefully reviewed and selected from 97 initial submissions. The volume features contributions from both classical theory fields and application areas (bioinformatics, systems biology, language technology, artificial intelligence, etc.). Among the topics covered are algebraic language theory; algorithms for semi-structured data mining; algorithms on automata and words; automata and logic; automata for system analysis and program verification; automata, concurrency and Petri nets; automatic structures; cellular automata; combinatorics on words; computability; computational complexity; computational linguistics; data and image compression; decidability questions on words and languages; descriptional complexity; DNA and other models of bio-inspired computing; document engineering; foundations of finite state technology; foundations of XML; fuzzy and rough languages; grammars (Chomsky hierarchy, contextual, multidimensional, unification, categorial, etc.); grammars and automata architectures; grammatical inference and algorithmic learning; graphs and graph transformation; language varieties and semigroups; language-based cryptography; language-theoretic foundations of artificial intelligence and artificial life; parallel and regulated rewriting; parsing; pattern recognition; patterns and codes; power series; quantum, chemical and optical computing; semantics; string and combinatorial issues in computational biology and bioinformatics; string processing algorithms; symbolic dynamics; symbolic neural networks; term rewriting; transducers; trees, tree languages and tree automata; weighted automata.

This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

Author : Peter Kritzer
ISBN : 9783110317930
Genre : Mathematics
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This book is summarizing the results of the workshop "Uniform Distribution and Quasi-Monte Carlo Methods" of the RICAM Special Semester on "Applications of Algebra and Number Theory" in October 2013. The survey articles in this book focus on number theoretic point constructions, uniform distribution theory, and quasi-Monte Carlo methods. As deterministic versions of the Monte Carlo method, quasi-Monte Carlo rules enjoy increasing popularity, with many fruitful applications in mathematical practice, as for example in finance, computer graphics, and biology. The goal of this book is to give an overview of recent developments in uniform distribution theory, quasi-Monte Carlo methods, and their applications, presented by leading experts in these vivid fields of research.

If the Mark I itself was a milestone in digital computing, so was this Manual: it was one of the first publications to address the fundamental question of how to get a computer to solve problems.

This book is devoted to recent developments in symbolic dynamics, and it comprises eight chapters. The first two are concerned with the study of symbolic sequences of "low complexity," the following two introduce "high complexity" systems. Chapter five presents results on asymptotic laws for the random times of occurrence of rare events. Chapter six deals with diophantine problems and combinatorial Ramsey theory. Chapter seven looks at the dynamics of symbolic systems arising from numeration systems, and chapter eight gives a complete description of the symbolic dynamics of Lorenz maps.

Author : T. Helleseth
ISBN : 9781447106739
Genre : Mathematics
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Pseudorandom sequences have widespread applications, for instance, in spread spectrum, code division multiple access, optical and ultrawide band communication systems, as well as in ranging systems global positioning systems, circuit testing and stream ciphers. Such sequences also have strong ties to error-correcting codes. This volume contains survey and research papers on sequences and their applications. It brings together leading experts from discrete mathematics, computer science and communications engineering, and helps to bridge advances in these different areas. Papers in this volume discuss the theory of sequences and their applications in cryptography, coding theory, communications systems, numerical computation and computer simulation.

Author : N. Pytheas Fogg
ISBN : 9783540457145
Genre : Mathematics
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A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.

Author : Huzihiro Araki
ISBN : 079232532X
Genre : Science
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In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.

Author : Michel Rigo
ISBN : 9781119042860
Genre : Technology & Engineering
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The interplay between words, computability, algebra andarithmetic has now proved its relevance and fruitfulness. Indeed,the cross-fertilization between formal logic and finite automata(such as that initiated by J.R. Büchi) or betweencombinatorics on words and number theory has paved the way torecent dramatic developments, for example, the transcendenceresults for the real numbers having a “simple” binaryexpansion, by B. Adamczewski and Y. Bugeaud. This book is at the heart of this interplay through a unifiedexposition. Objects are considered with a perspective that comesboth from theoretical computer science and mathematics. Theoreticalcomputer science offers here topics such as decision problems andrecognizability issues, whereas mathematics offers concepts such asdiscrete dynamical systems. The main goal is to give a quick access, for students andresearchers in mathematics or computer science, to actual researchtopics at the intersection between automata and formal languagetheory, number theory and combinatorics on words. The second of two volumes on this subject, this book coversregular languages, numeration systems, formal methods applied todecidability issues about infinite words and sets of numbers.

Author : Michel Rigo
ISBN : 9781119008224
Genre : Computers
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Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidable regularities or patterns. When considering some numeration systems, any integer can be represented as a finite word over an alphabet of digits. This simple observation leads to the study of the relationship between the arithmetical properties of the integers and the syntactical properties of the corresponding representations. One of the most profound results in this direction is given by the celebrated theorem by Cobham. Surprisingly, a recent extension of this result to complex numbers led to the famous Four Exponentials Conjecture. This is just one example of the fruitful relationship between formal language theory (including the theory of automata) and number theory.

Author : Valerie Manusov
ISBN : 1412904048
Genre : Language Arts & Disciplines
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This Handbook provides an up-to-date discussion of the central issues in nonverbal communication and examines the research that informs these issues. Editors Valerie Manusov and Miles Patterson bring together preeminent scholars, from a range of disciplines, to reveal the strength of nonverbal behavior as an integral part of communication.

This book is about anaerobic microbes that inhabit the gut of ruminants. Similar microbes are found in many other ecosystems, including other animals and man and engineered systems such as waste digesters and landfill. This book is therefore a comprehensive reference work concerned with microbes which are of fundamental importance. They are the focal points for future developments in agriculture, industrial fermenatations, the monitoring and control of environmental pollution and the health and well-being of man.

Author : Burkhard Monien
ISBN : 3540508406
Genre : Computers
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This volume contains the presentations of the Sixth Symposium on Theoretical Aspects of Computer Science (STACS 89) held at the University of Paderborn, February 16-18, 1989. In addition to papers presented in the regular program the volume contains abstracts of software systems demonstrations which were included in this conference series in order to show applications of research results in theoretical computer science. The papers are grouped into the following thematic sections: computational geometry, automata theory and formal languages, semantics of programming languages, parallel algorithms, graph algorithms, complexity, structures, fault tolerance, completeness, distributed computing and concurrency.

Author : Hans Eysenck
ISBN : 9781468422443
Genre : Psychology
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This is a book on reminiscence, or more modestly a book on reminiscence in motor tasks, or more modestly still on reminiscence in pursuit rotor learning, with occasional references to other types of reminiscence. The vast majority of experiments investigating reminiscence with the pur suit rotor have been carried out within the framework of Hullian learn ing theory. Thus, of necessity, this book also will be much concerned with that theory. Some readers may feel that so much detailed attention paid to one piece of apparatus and one now rather discredited theory, is overdone; we could not agree with such an evaluation. There are several features of pursuit-rotor performance which make it particularly worthy of attention. One of the more important of these features is the easy replicability of many of the phenomena found in performance of this task; this is our first point. Replicability is the life blood of science; what cannot be replicated by any well-trained observer is of doubtful status in science, and on this score pursuit-rotor work certainly emerges as perhaps the most reliable set of observations in experimental psychology. The effects of massing and spacing; of rest pauses of different length; of switching from massed to spaced learn ing, or vice versa; of interpolating different activities; of introducing distracting stimuli; of switching from right to left hand, or vice versa; of changing the speed of rotation, or the diameter of the target disk these are clear-cut and replicable as few phenomena in psychology are.

This series is devoted to significant topics or themes that have wide application in mathematics or mathematical science and for which a detailed development of the abstract theory is less important than a thorough and concrete exploration of the implications and applications. Books in the Encyclopedia of Mathematics and its Applications cover their subjects comprehensively. Less important results may be summarised as exercises at the ends of chapters, For technicalities, readers can be referred to the bibliography, which is expected to be comprehensive. As a result, volumes are encyclopedic references or manageable guides to major subjects.

Author : W. R. Croasmun
ISBN : 0471185930
Genre : Science
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This volume covers the new methodological advances in NMR spectroscopy that have been developed since the publication of the first edition. These include: 'indirect detection' methods, particularly proton-detected carbon-13 spectra, which have profoundly increased NMR sensitivities; 3- and even higher- dimensional NMR methods which have further increased spectral resolving and correlating power; powerful new computer programs which assist in all phases of data analysis and ultimately make possible rigorous interpretations of complex 2D and higher- dimensional NMR spectra using molecular mechanics and dynamics calculations; and field gradient technology which makes it possible to acquire 2D and higher-dimensional spectra of concentrated samples very rapidly, greatly reducing experiment times. This new edition retains the original format of the first edition with introductory chapters covering descriptions, basic theoretical treatments and experimental aspects of the methods. These are followed by applications chapters representing a broad sampling of important research areas and compound classes