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Combinatorics Words and Symbolic Dynamics

Combinatorics  Words and Symbolic Dynamics Author Valérie Berthé
ISBN-10 9781316462522
Release 2016-02-26
Pages
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Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include combinatorics on words, pattern avoidance, graph theory, tilings and theory of computation, multidimensional subshifts, discrete dynamical systems, ergodic theory, numeration systems, dynamical arithmetics, automata theory and synchronised words, analytic combinatorics, continued fractions and probabilistic models. Each topic is presented in a way that links it to the main themes, but then they are also extended to repetitions in words, similarity relations, cellular automata, friezes and Dynkin diagrams. The book will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, tilings and stringology. It will also interest biologists using text algorithms.



Combinatorics Automata and Number Theory

Combinatorics  Automata and Number Theory Author Valérie Berthé
ISBN-10 9780521515979
Release 2010-08-12
Pages 615
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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.



Sequences Groups and Number Theory

Sequences  Groups  and Number Theory Author Valérie Berthé
ISBN-10 9783319691527
Release 2018-04-09
Pages 578
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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.



Algebraic Combinatorics on Words

Algebraic Combinatorics on Words Author M. Lothaire
ISBN-10 0521812208
Release 2002-04-18
Pages 504
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Comprehensive 2002 introduction to combinatorics on words for mathematicians and theoretical computer scientists.



Pursuit of the Universal

Pursuit of the Universal Author Arnold Beckmann
ISBN-10 9783319401898
Release 2016-06-13
Pages 375
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This book constitutes the refereed proceedings of the 12th Conference on Computability in Europe, CiE 2016, held in Paris, France, in June/July 2016. The 18 revised full papers and 19 invited papers and invited extended abstracts were carefully reviewed and selected from 40 submissions. The conference CiE 2016 has six special sessions – two sessions, cryptography and information theory and symbolic dynamics, are organized for the first time in the conference series. In addition to this new developments in areas frequently covered in the CiE conference series were addressed in the following sessions: computable and constructive analysis; computation in biological systems; history and philosophy of computing; weak arithmetic.



Advanced Graph Theory and Combinatorics

Advanced Graph Theory and Combinatorics Author Michel Rigo
ISBN-10 9781848216167
Release 2016-12-27
Pages 290
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Advanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of the book covers basic material related to linear recurrence relations with application to counting and the asymptotic estimate of the rate of growth of a sequence satisfying a recurrence relation.



Codes and Automata

Codes and Automata Author Jean Berstel
ISBN-10 9780521888318
Release 2010-01
Pages 619
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This major revision of Berstel and Perrin's classic Theory of Codes has been rewritten with a more modern focus and a much broader coverage of the subject. The concept of unambiguous automata, which is intimately linked with that of codes, now plays a significant role throughout the book, reflecting developments of the last 20 years. This is complemented by a discussion of the connection between codes and automata, and new material from the field of symbolic dynamics. The authors have also explored links with more practical applications, including data compression and cryptography. The treatment remains self-contained: there is background material on discrete mathematics, algebra and theoretical computer science. The wealth of exercises and examples make it ideal for self-study or courses. In summary, this is a comprehensive reference on the theory of variable-length codes and their relation to automata.



Formal Languages Automata and Numeration Systems

Formal Languages  Automata and Numeration Systems Author Michel Rigo
ISBN-10 9781119008224
Release 2014-09-10
Pages 338
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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. Contents to include: • algebraic structures, homomorphisms, relations, free monoid • finite words, prefixes, suffixes, factors, palindromes • periodicity and Fine–Wilf theorem • infinite words are sequences over a finite alphabet • properties of an ultrametric distance, example of the p-adic norm • topology of the set of infinite words • converging sequences of infinite and finite words, compactness argument • iterated morphism, coding, substitutive or morphic words • the typical example of the Thue–Morse word • the Fibonacci word, the Mex operator, the n-bonacci words • wordscomingfromnumbertheory(baseexpansions,continuedfractions,...) • the taxonomy of Lindenmayer systems • S-adic sequences, Kolakoski word • repetition in words, avoiding repetition, repetition threshold • (complete) de Bruijn graphs • concepts from computability theory and decidability issues • Post correspondence problem and application to mortality of matrices • origins of combinatorics on words • bibliographic notes • languages of finite words, regular languages • factorial, prefix/suffix closed languages, trees and codes • unambiguous and deterministic automata, Kleene’s theorem • growth function of regular languages • non-deterministic automata and determinization • radix order, first word of each length and decimation of a regular language • the theory of the minimal automata • an introduction to algebraic automata theory, the syntactic monoid and the syntactic complexity • star-free languages and a theorem of Schu ̈tzenberger • rational formal series and weighted automata • context-free languages, pushdown automata and grammars • growth function of context-free languages, Parikh’s theorem • some decidable and undecidable problems in formal language theory • bibliographic notes • factor complexity, Morse–Hedlund theorem • arithmetic complexity, Van Der Waerden theorem, pattern complexity • recurrence, uniform recurrence, return words • Sturmian words, coding of rotations, Kronecker’s theorem • frequencies of letters, factors and primitive morphism • critical exponent • factor complexity of automatic sequences • factor complexity of purely morphic sequences • primitive words, conjugacy, Lyndon word • abelianisation and abelian complexity • bibliographic notes • automatic sequences, equivalent definitions • a theorem of Cobham, equivalence of automatic sequences with constant length morphic sequences • a few examples of well-known automatic sequences • about Derksen’s theorem • some morphic sequences are not automatic • abstract numeration system and S-automatic sequences • k − ∞-automatic sequences • bibliographic notes • numeration systems, greedy algorithm • positional numeration systems, recognizable sets of integers • divisibility criterion and recognizability of N • properties of k-recognizable sets of integers, ratio and difference of consec- utive elements: syndeticity • integer base and Cobham’s theorem on the base dependence of the recog- nizability • non-standard numeration systems based on sequence of integers • linear recurrent sequences, Loraud and Hollander results • Frougny’s normalization result and addition • morphic numeration systems/sets of integers whose characteristic sequence is morphic • towards a generalization of Cobham’s theorem • a few words on the representation of real numbers, β-integers, finiteness properties • automata associated with Parry numbers and numeration systems • bibliographic notes First order logic • Presburger arithmetic and decidable theory • Muchnik’s characterization of semi-linear sets • Bu ̈chi’s theorem: k-recognizable sets are k-definable • extension to Pisot numeration systems • extension to real numbers • decidability issues for numeration systems • applications in combinatorics on words



Annual Symposium on Theoretical Aspects of Computer Science

Annual Symposium on Theoretical Aspects of Computer Science Author
ISBN-10 UOM:39015058765796
Release 2006
Pages
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Annual Symposium on Theoretical Aspects of Computer Science has been writing in one form or another for most of life. You can find so many inspiration from Annual Symposium on Theoretical Aspects of Computer Science also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Annual Symposium on Theoretical Aspects of Computer Science book for free.



Ars Combinatoria

Ars Combinatoria Author
ISBN-10 UOM:39015059041163
Release 2005
Pages
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Ars Combinatoria has been writing in one form or another for most of life. You can find so many inspiration from Ars Combinatoria also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Ars Combinatoria book for free.



Complex Analysis and Digital Geometry

Complex Analysis and Digital Geometry Author Mikael Passare
ISBN-10 9155476724
Release 2009
Pages 364
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Complex Analysis and Digital Geometry has been writing in one form or another for most of life. You can find so many inspiration from Complex Analysis and Digital Geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Complex Analysis and Digital Geometry book for free.



Orthogonal Polynomials of Several Variables

Orthogonal Polynomials of Several Variables Author Charles F. Dunkl
ISBN-10 0521800439
Release 2001-02-22
Pages 390
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Orthogonal polynomials of several variables, approximation theory, symmetry-group methods.



Bulletin of the Belgian Mathematical Society Simon Stevin

Bulletin of the Belgian Mathematical Society  Simon Stevin Author
ISBN-10 UOM:39015059031875
Release 2003
Pages
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Encyclopaedia of Mathematics

Encyclopaedia of Mathematics Author Michiel Hazewinkel
ISBN-10 0792347099
Release 1997-08-31
Pages 588
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The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics and is now available on CD-ROM. The CD-ROM edition contains all the articles published in the 10-Volume set and the first Supplementary volume. All articles are hyperlinked and some animation and 3D objects have been added. Presentation and navigation is managed by Dynatext and an advanced search engine allows for full text search, searching with wildcards, Boolean search, proximity search and structure-aware searches. All text can be printed and exported. The CD-ROM is available in two versions: a network version for PC and Unix platforms, and a stand-alone version for PC and Mac platforms only.



JMSJ

JMSJ Author Nihon Sūgakkai
ISBN-10 UCSC:32106018227337
Release 2007
Pages
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JMSJ has been writing in one form or another for most of life. You can find so many inspiration from JMSJ also informative, and entertaining. Click DOWNLOAD or Read Online button to get full JMSJ book for free.



Special Functions

Special Functions Author George E. Andrews
ISBN-10 0521789885
Release 1999
Pages 664
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An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.



Discrete Mathematics and Its Applications

Discrete Mathematics and Its Applications Author Kenneth Rosen
ISBN-10 9780077418939
Release 1995
Pages
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Discrete Mathematics and Its Applications has been writing in one form or another for most of life. You can find so many inspiration from Discrete Mathematics and Its Applications also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Discrete Mathematics and Its Applications book for free.