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Author: Uno Kaljulaid Publisher: IOS Press ISBN: 1586035827 Category : Computers Languages : en Pages : 496
Book Description
This volume provides a selection of previously published papers and manuscripts of Uno Kaljulaid, an eminent Estonian algebraist of the last century. The central part of the book is the English translation of Kaljulaid's 1979 Candidate thesis, which originally was typewritten in Russian and manufactured in not so many copies. The thesis is devoted to representation theory in the spirit of his thesis advisor B.I. Plotkin: representations of semigroups and algebras, especially extension to this situation, and application of the notion of triangular product of representations for groups introduced by Plotkin. Through representation theory, Kaljulaid became also interested in automata theory, which at a later phase became his main area of interest. Another field of research concerns combinatorics. Besides being an outstanding and most dedicated mathematician, Uno Kaljulaid was also very much interested in the history of mathematics. In particular, he took a vivid interest in the life and work of the great 19th century Dorpat-Tartu algebraist Th. Molien. Kaljulaid was also very interested in teaching and exposition, or popularization of mathematics. Some of his more popular-scientific papers were published in an Estonian language journal Matemaatika ja Kaasaeg (Mathematics and Our Age). Among them, there is a whole series of papers about algebraic matters, culminating in a brilliant, elementary - although partly rather philosophical - essay devoted to Galois theory. Another such series is his excellent essay of Diophantine Geometry in various installments, followed by his loge to another of his teachers Yu. I. Manin. It is believed that the inclusion of these papers here will make it more interesting for beginners, and perhaps even contribute to attracting young people to mathematics.
Author: Uno Kaljulaid Publisher: IOS Press ISBN: 1586035827 Category : Computers Languages : en Pages : 496
Book Description
This volume provides a selection of previously published papers and manuscripts of Uno Kaljulaid, an eminent Estonian algebraist of the last century. The central part of the book is the English translation of Kaljulaid's 1979 Candidate thesis, which originally was typewritten in Russian and manufactured in not so many copies. The thesis is devoted to representation theory in the spirit of his thesis advisor B.I. Plotkin: representations of semigroups and algebras, especially extension to this situation, and application of the notion of triangular product of representations for groups introduced by Plotkin. Through representation theory, Kaljulaid became also interested in automata theory, which at a later phase became his main area of interest. Another field of research concerns combinatorics. Besides being an outstanding and most dedicated mathematician, Uno Kaljulaid was also very much interested in the history of mathematics. In particular, he took a vivid interest in the life and work of the great 19th century Dorpat-Tartu algebraist Th. Molien. Kaljulaid was also very interested in teaching and exposition, or popularization of mathematics. Some of his more popular-scientific papers were published in an Estonian language journal Matemaatika ja Kaasaeg (Mathematics and Our Age). Among them, there is a whole series of papers about algebraic matters, culminating in a brilliant, elementary - although partly rather philosophical - essay devoted to Galois theory. Another such series is his excellent essay of Diophantine Geometry in various installments, followed by his loge to another of his teachers Yu. I. Manin. It is believed that the inclusion of these papers here will make it more interesting for beginners, and perhaps even contribute to attracting young people to mathematics.
Author: Dominique Perrin Publisher: Academic Press ISBN: 9780125321112 Category : Computers Languages : en Pages : 560
Book Description
Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic. Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Büchi, McNaughton and Schützenberger. Serves as both an introduction to the field and as a reference book. Contains numerous exercises desgined to aid students and readers. Self-contained chapters provide helpful guidance for lectures.
Author: John L. Rhodes Publisher: World Scientific ISBN: 9812836969 Category : Mathematics Languages : en Pages : 293
Book Description
This book was originally written in 1969 by Berkeley mathematician John Rhodes. It is the founding work in what is now called algebraic engineering, an emerging field created by using the unifying scheme of finite state machine models and their complexity to tie together many fields: finite group theory, semigroup theory, automata and sequential machine theory, finite phase space physics, metabolic and evolutionary biology, epistemology, mathematical theory of psychoanalysis, philosophy, and game theory. The author thus introduced a completely original algebraic approach to complexity and the understanding of finite systems. The unpublished manuscript, often referred to as "The Wild Book," became an underground classic, continually requested in manuscript form, and read by many leading researchers in mathematics, complex systems, artificial intelligence, and systems biology. Yet it has never been available in print until now. This first published edition has been edited and updated by Chrystopher Nehaniv for the 21st century. Its novel and rigorous development of the mathematical theory of complexity via algebraic automata theory reveals deep and unexpected connections between algebra (semigroups) and areas of science and engineering. Co-founded by John Rhodes and Kenneth Krohn in 1962, algebraic automata theory has grown into a vibrant area of research, including the complexity of automata, and semigroups and machines from an algebraic viewpoint, and which also touches on infinite groups, and other areas of algebra. This book sets the stage for the application of algebraic automata theory to areas outside mathematics. The material and references have been brought up to date bythe editor as much as possible, yet the book retains its distinct character and the bold yet rigorous style of the author. Included are treatments of topics such as models of time as algebra via semigroup theory; evolution-complexity relations applicable to both ontogeny and evolution; an approach to classification of biological reactions and pathways; the relationships among coordinate systems, symmetry, and conservation principles in physics; discussion of "punctuated equilibrium" (prior to Stephen Jay Gould); games; and applications to psychology, psychoanalysis, epistemology, and the purpose of life. The approach and contents will be of interest to a variety of researchers and students in algebra as well as to the diverse, growing areas of applications of algebra in science and engineering. Moreover, many parts of the book will be intelligible to non-mathematicians, including students and experts from diverse backgrounds.
Author: Gracinda M. S. Gomes Publisher: World Scientific ISBN: 9789812776884 Category : Mathematics Languages : en Pages : 536
Book Description
The thematic term on OC Semigroups, Algorithms, Automata and LanguagesOCO organized at the International Centre of Mathematics (Coimbra, Portugal) in MayOCoJuly 2001 was the gathering point for researchers working in the field of semigroups, algorithms, automata and languages. These areas were selected considering their huge recent developments, their potential applications, and the motivation from other fields of mathematics and computer science. This proceedings volume is a unique collection of advanced courses and original contributions on semigroups and their connections with logic, automata, languages, group theory, discrete dynamics, topology and complexity. A selection of open problems discussed during the thematic term is also included. Contents: Finite Semigroups: An Introduction to a Unified Theory of Pseudovarieties (J Almeida); On Existence Varieties of Regular Semigroups (K Auinger); Varieties of Languages (M J J Branco); A Short Introduction to Automatic Group Theory (C Choffrut); Some Results on Semigroup-Graded Rings (W D Munn); Profinite Groups and Applications to Finite Semigroups (L Ribes); Dynamics of Finite Semigroups (J Almeida); Finite Semigroups Imposing Tractable Constraints (A Bulatov et al.); On the Efficiency and Deficiency of Rees Matrix Semigroups (C M Campbell et al.); Some Pseudovariety Joins Involving Groups and Locally Trivial Semigroups (J C Costa); Partial Action of Groups on Relational Structures: A Connection Between Model Theory and Profinite Topology (T Coulbois); Some Relatives of Automatic and Hyperbolic Groups (M Hoffmann et al.); A Sampler of a Topological Approach to Inverse Semigroups (B Steinberg); Finite Semigroups and the Logical Description of Regular Languages (H Straubing); Diamonds are Forever: The Variety DA (P Tesson & D Th(r)rien); Decidability Problems in Finite Semigroups (P G Trotter); and other papers. Readership: Researchers, academics and graduate students in pure mathematics and computer science."
Author: P.A. Grillet Publisher: Springer Science & Business Media ISBN: 1475733895 Category : Mathematics Languages : en Pages : 443
Book Description
This is the first book about commutative semigroups in general. Emphasis is on structure but the other parts of the theory are at least surveyed and a full set of about 850 references is included. The book is intended for mathematicians who do research on semigroups or who encounter commutative semigroups in their research.
Author: John N. Mordeson Publisher: Springer ISBN: 3540371257 Category : Mathematics Languages : en Pages : 324
Book Description
Lotfi Zadeh introduced the notion of a fuzzy subset of a set in 1965. Ris seminal paper has opened up new insights and applications in a wide range of scientific fields. Azriel Rosenfeld used the notion of a fuzzy subset to put forth cornerstone papers in several areas of mathematics, among other discplines. Rosenfeld is the father of fuzzy abstract algebra. Kuroki is re sponsible for much of fuzzy ideal theory of semigroups. Others who worked on fuzzy semigroup theory, such as Xie, are mentioned in the bibliogra phy. The purpose of this book is to present an up to date account of fuzzy subsemigroups and fuzzy ideals of a semigroup. We concentrate mainly on theoretical aspects, but we do include applications. The applications are in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. An extensive account of fuzzy automata and fuzzy languages is given in [100]. Consequently, we only consider results in these areas that have not appeared in [100] and that pertain to semigroups. In Chapter 1, we review some basic results on fuzzy subsets, semigroups, codes, finite state machines, and languages. The purpose of this chapter is to present basic results that are needed in the remainder of the book. In Chapter 2, we introduce certain fuzzy ideals of a semigroup, namely, fuzzy two-sided ideals, fuzzy bi-ideals, fuzzy interior ideals, fuzzy quasi ideals, and fuzzy generalized bi-ideals.
Author: Abraham Ginzburg Publisher: Academic Press ISBN: 148322516X Category : Technology & Engineering Languages : en Pages : 176
Book Description
Algebraic Theory of Automata provides information pertinent to the methods and results of algebraic theory of automata. This book covers a variety of topics, including sets, semigroup, groupoids, isomorphism, semiautomata, proof of Kleene's theorem, and algebraic manipulations. Organized into seven chapters, this book begins with an overview of the fundamental properties of groups and semigroups. This text then examines the notion of semiautomaton, which serves as a basis for a rich and interesting theory. Other chapters consider algebraic notions and methods that are very useful in dealing with semiautomata. This book discusses as well some properties of the notion of covering of semiautomata. The final chapter deals with the theory of Krohn and Rhodes. This book is a valuable resource for graduate students.
Author: Mark V. Sapir Publisher: Springer ISBN: 3319080318 Category : Mathematics Languages : en Pages : 369
Book Description
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.
Author: Uno Kaljulaid
Author: Uno Kaljulaid
Author: Dominique Perrin
Author: John L. Rhodes
Author: M. Holcombe
Author: Gracinda M. S. Gomes
Author: 
Author: P.A. Grillet
Author: John N. Mordeson
Author: Abraham Ginzburg
Author: Mark V. Sapir