Computation and Automata

Author: Arto Salomaa
Publisher: Cambridge University Press
ISBN: 9780521302456
Format: PDF
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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.

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.

Codes and Automata

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

Computation with Finitely Presented Groups

Author: Charles C. Sims
Publisher: Cambridge University Press
ISBN: 9780521432139
Format: PDF, Mobi
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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.

Applied Combinatorics on Words

Author: M. Lothaire
Publisher: Cambridge University Press
ISBN: 9780521848022
Format: PDF
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Applications of combinatorics in bioformatics, text processing, combinatorial enumeration and fractal analysis.

Algebraic Combinatorics on Words

Author: M. Lothaire
Publisher: Cambridge University Press
ISBN: 9780521812207
Format: PDF
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Comprehensive 2002 introduction to combinatorics on words for mathematicians and theoretical computer scientists.

Relational Mathematics

Author: Gunther Schmidt
Publisher: Cambridge University Press
ISBN: 0521762685
Format: PDF, Kindle
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A modern, comprehensive 2010 overview providing an easy introduction for applied scientists who are not versed in mathematics.

Combinatorics Words and Symbolic Dynamics

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

Unconventional Computation

Author: Cristian S. Calude
Publisher: Springer Science & Business Media
ISBN: 3642213405
Format: PDF
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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.

Permanents

Author: Henryk Minc
Publisher: Cambridge University Press
ISBN: 9780521302265
Format: PDF, Kindle
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The purpose of this book, which was first published in 1978, is to give a complete account of the theory of permanents, their history and applications. This volume was the first complete account of the theory of permanents, covering virtually the whole of the subject, a feature that no simple survey of the theory of matrices can even attempt. The work also contains many results stated without formal proofs. This book can be used as a textbook at the advanced undergraduate or graduate level. The only prerequisites are a standard undergraduate course in the theory of matrices and a measure of mathematical maturity.