Semigroups And Combinatorial Applications
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Semigroups And Combinatorial Applications
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Author : Gerard Lallement
language : en
Publisher: John Wiley & Sons
Release Date : 1979
Semigroups And Combinatorial Applications written by Gerard Lallement and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
The purpose of this book is to present those parts of the theory of semigroups that are directly related to automata theory, algebraic linguistics, and combinatorics. Publications in these mathematical disciplines contained methods and results pertaining to the algebraic theory of semigroups, and this has contributed to considerable enrichment of the theory, enlargement of its scope, and improved its potential to become a major domain of algebra. Semigroup theory appears to provide a general framework for unifying and clarifying a number of topics in fields that at first sight appear unrelated. This book is intended as a textbook for graduate students in mathematics and computer science, and as a reference book for researchers interested in associative structures.
Topics On Combinatorial Semigroups
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Author : Yuqi Guo
language : en
Publisher: Springer Nature
Release Date : 2024-04-22
Topics On Combinatorial Semigroups written by Yuqi Guo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-22 with Mathematics categories.
By combinatorial semigroups, we mean a general term of concepts, facts and methods which are produced in investigating of algebraic and combinatorial properties, constructions, classifications and interrelations of formal languages and automata, codes, finite and infinite words by using semigroup theory and combinatorial analysis. The main research objects in this field are the elements and subsets of the free semigroups and monoids and many combinatorial properties of these objects, which are closely related to algebraic theory of semigroups. This book first introduces some basic concepts and notations in combinatorial semigroups. Since many contents involving the constructions of (generalized) disjunctive languages and regular languages are closely related to the algebraic theory of codes, some selected topics are introduced in the following chapter, including the method of defining codes by using dependence systems, the maximality and completeness of codes, and the detailed discussion of some special kinds of codes such as convex codes, semaphore codes and solid codes. Then the remaining chapters present the main topics of the book - regular languages, disjunctive languages, and their various kinds of generalizations. This book might be useful to researchers in mathematics who are interested in combinatorial semigroups.
Semigroups Algebraic Theory And Applications To Formal Languages And Codes
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Author : Celestina Bonzini
language : en
Publisher: World Scientific
Release Date : 1993-10-29
Semigroups Algebraic Theory And Applications To Formal Languages And Codes written by Celestina Bonzini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-29 with categories.
The proceedings present some new topics and techniques of semigroup theory. Papers by leading experts in this theory are collected. Since results on semigroups have naturally been employed in formal languages and codes, the focus is also on these directions.
Semigroups And Their Applications
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Author : Simon M. Goberstein
language : en
Publisher: Springer Science & Business Media
Release Date : 1987-04-30
Semigroups And Their Applications written by Simon M. Goberstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-04-30 with Mathematics categories.
Most papers published in this volume are based on lectures presented at the Chico Conference on Semigroups held on the Chico campus of the Cal ifornia State University on April 10-12, 1986. The conference was spon sored by the California State University, Chico in cooperation with the Engineering Computer Sciences Department of the Pacific Gas and Electric Company. The program included seven 50-minute addresses and seventeen 30-minute lectures. Speakers were invited by the organizing committee consisting of S. M. Goberstein and P. M. Higgins. The purpose of the conference was to bring together some of the leading researchers in the area of semigroup theory for a discussion of major recent developments in the field. The algebraic theory of semigroups is growing so rapidly and new important results are being produced at such a rate that the need for another meeting was well justified. It was hoped that the conference would help to disseminate new results more rapidly among those working in semi groups and related areas and that the exchange of ideas would stimulate research in the subject even further. These hopes were realized beyond all expectations.
Handbook Of Formal Languages
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Author : Grzegorz Rozenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 1997
Handbook Of Formal Languages written by Grzegorz Rozenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Computers categories.
This uniquely authoritative and comprehensive handbook is the first work to cover the vast field of formal languages, as well as their applications to the divergent areas of linguistics, dvelopmental biology, computer graphics, cryptology, molecular genetics, and programming languages. The work has been divided into three volumes.
Classical Finite Transformation Semigroups
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Author : Olexandr Ganyushkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
Classical Finite Transformation Semigroups written by Olexandr Ganyushkin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Mathematics categories.
The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed first of all to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but also to tutors and researchers.
Formal Properties Of Finite Automata And Applications
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Author : Jean E. Pin
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-10-11
Formal Properties Of Finite Automata And Applications written by Jean E. Pin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-10-11 with Computers categories.
The volume contains the proceedings of the 16th Spring School on Theoretical Computer Science held in Ramatuelle, France, in May 1988. It is a unique combination of research level articles on various aspects of the theory of finite automata and its applications. Advances made in the last five years on the mathematical foundations form the first part of the book. The second part is devoted to the important problems of the theory including star-height, concatenation hierarchies, and connections with logic and word problems. The last part presents a large variety of possible applications: number theory, distributed systems, algorithms on strings, theory of codes, complexity of boolean circuits and others.
Combinatorial Algebra Syntax And Semantics
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Author : Mark V. Sapir
language : en
Publisher: Springer
Release Date : 2014-10-06
Combinatorial Algebra Syntax And Semantics written by Mark V. Sapir and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-06 with Mathematics categories.
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.
Lattices Semigroups And Universal Algebra
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Author : Jorge Almeida
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Lattices Semigroups And Universal Algebra written by Jorge Almeida and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
This volume contains papers which, for the most part, are based on talks given at an international conference on Lattices, Semigroups, and Universal Algebra that was held in Lisbon, Portugal during the week of June 20-24, 1988. The conference was dedicated to the memory of Professor Antonio Almeida Costa, a Portuguese mathematician who greatly contributed to the development of th algebra in Portugal, on the 10 anniversary of his death. The themes of the conference reflect some of his research interests and those of his students. The purpose of the conference was to gather leading experts in Lattices, Semigroups, and Universal Algebra and to promote a discussion of recent developments and trends in these areas. All three fields have grown rapidly during the last few decades with varying degrees of interaction. Lattice theory and Universal Algebra have historically evolved alongside with a large overlap between the groups of researchers in the two fields. More recently, techniques and ideas of these theories have been used extensively in the theory of semigroups. Conversely, some developments in that area may inspire further developments in Universal Algebra. On the other hand, techniques of semi group theory have naturally been employed in the study of semilattices. Several papers in this volume elaborate on these interactions.
Profinite Semigroups And Symbolic Dynamics
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Author : Jorge Almeida
language : en
Publisher: Springer Nature
Release Date : 2020-09-10
Profinite Semigroups And Symbolic Dynamics written by Jorge Almeida and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-10 with Mathematics categories.
This book describes the relation between profinite semigroups and symbolic dynamics. Profinite semigroups are topological semigroups which are compact and residually finite. In particular, free profinite semigroups can be seen as the completion of free semigroups with respect to the profinite metric. In this metric, two words are close if one needs a morphism on a large finite monoid to distinguish them. The main focus is on a natural correspondence between minimal shift spaces (closed shift-invariant sets of two-sided infinite words) and maximal J-classes (certain subsets of free profinite semigroups). This correspondence sheds light on many aspects of both profinite semigroups and symbolic dynamics. For example, the return words to a given word in a shift space can be related to the generators of the group of the corresponding J-class. The book is aimed at researchers and graduate students in mathematics or theoretical computer science.