Computation and Automata

Author: Arto Salomaa
Publisher: Cambridge University Press
ISBN: 9780521302456
Format: PDF, ePub
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In this book, which was originally published in 1985, Arto Salomaa gives an introduction to certain mathematical topics central to theoretical computer science: computability and recursive functions, formal languages and automata, computational complexity and cryptography.

Computation with Finitely Presented Groups

Author: Charles C. Sims
Publisher: Cambridge University Press
ISBN: 9780521432139
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Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.

Unconventional Computation

Author: Cristian S. Calude
Publisher: Springer Science & Business Media
ISBN: 3642213405
Format: PDF, ePub, Mobi
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This book constitutes the refereed proceedings of the 10th International Conference on Unconventional Computation, UC 2011, held in Turku, Finland, in June 2011. The 17 revised full papers presented together with 6 extended abstracts of invited talks, and 3 extended abstracts of tutorials were carefully reviewed and selected from 33 initial submissions. The papers are devoted to all aspects of unconventional computation theory as well as experiments and applications. Typical topics are: natural computing including quantum, cellular, molecular, membrane, neural, and evolutionary computing, as well as chaos and dynamical system-based computing, and various proposals for computational mechanisms that go beyond the Turing model.

Combinatorics Automata and Number Theory

Author: Valérie Berthé
Publisher: Cambridge University Press
ISBN: 0521515971
Format: PDF, Kindle
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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.

Theory and Practice of Natural Computing

Author: Adrian-Horia Dediu
Publisher: Springer
ISBN: 3642338607
Format: PDF, ePub, Docs
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This book constitutes the refereed proceedings of the First International Conference, TPNC 2012, held in Tarragona, Spain, in October 2012. The 12 revised full papers presented together with 6 invited talks were carefully reviewed and selected from 34 submissions. The papers are organized in topical sections on nature-inspired models of computation; synthesizing nature by means of computation; nature-inspired materials; and information processing in nature.

Developments in Language Theory

Author: Masami Ito
Publisher: Springer Science & Business Media
ISBN: 3540404317
Format: PDF, Docs
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The refereed proceedings of the 6th International Conference on Developments in Language Theory, DLT 2002, held in Kyoto, Japan in September 2002. The 28 revised full papers presented together with 8 invited papers were carefully reviewed and selected from 63 submissions. Among the topics addressed are grammars and acceptors for strings, graphs, arrays, etc; efficient algorithms for languages; combinatorial and algebraic properties of languages; decision problems; relations to complexity theory, logic picture description and analysis, DNA computing, cryptography, concurrency, quantum computing, and algebraic systems.

Formal Languages Automata and Numeration Systems

Author: Michel Rigo
Publisher: John Wiley & Sons
ISBN: 1119008220
Format: PDF, ePub, Docs
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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

Combinatorics Words and Symbolic Dynamics

Author: Valérie Berthé
Publisher: Cambridge University Press
ISBN: 1316462528
Format: PDF, Kindle
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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.

Codes and Automata

Author: Jean Berstel
Publisher: Cambridge University Press
ISBN: 052188831X
Format: PDF, Kindle
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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.