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Author : Valery B. Kudryavtsev
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 27,8 MB
Release : 2006-01-18
Category : Mathematics
ISBN : 1402038178
Semigroups, Automata, Universal Algebra, Varieties
Author : Jorge Almeida
Publisher : World Scientific
Page : 532 pages
File Size : 50,29 MB
Release : 1995-01-27
Category : Mathematics
ISBN : 9814501565
Motivated by applications in theoretical computer science, the theory of finite semigroups has emerged in recent years as an autonomous area of mathematics. It fruitfully combines methods, ideas and constructions from algebra, combinatorics, logic and topology. In simple terms, the theory aims at a classification of finite semigroups in certain classes called “pseudovarieties”. The classifying characteristics have both structural and syntactical aspects, the general connection between them being part of universal algebra. Besides providing a foundational study of the theory in the setting of arbitrary abstract finite algebras, this book stresses the syntactical approach to finite semigroups. This involves studying (relatively) free and profinite free semigroups and their presentations. The techniques used are illustrated in a systematic study of various operators on pseudovarieties of semigroups.
Author : Jürgen Dassow
Publisher : Walter de Gruyter GmbH & Co KG
Page : 148 pages
File Size : 43,10 MB
Release : 1982-01-14
Category : Computers
ISBN : 3112735870
No detailed description available for "Completeness Problems in the Structural Theory of Automata".
Author : B. Mikolajczak
Publisher : Elsevier
Page : 425 pages
File Size : 23,38 MB
Release : 1991-01-14
Category : Mathematics
ISBN : 0080867847
Automata Theory is part of computability theory which covers problems in computer systems, software, activity of nervous systems (neural networks), and processes of live organisms development. The result of over ten years of research, this book presents work in the following areas of Automata Theory: automata morphisms, time-varying automata, automata realizations and relationships between automata and semigroups. Aimed at those working in discrete mathematics and computer science, parts of the book are suitable for use in graduate courses in computer science, electronics, telecommunications, and control engineering. It is assumed that the reader is familiar with the basic concepts of algebra and graph theory.
Author : Andrei Kelarev
Publisher : CRC Press
Page : 388 pages
File Size : 47,52 MB
Release : 2003-07-08
Category : Mathematics
ISBN : 9780824747084
Graph algebras possess the capacity to relate fundamental concepts of computer science, combinatorics, graph theory, operations research, and universal algebra. They are used to identify nontrivial connections across notions, expose conceptual properties, and mediate the application of methods from one area toward questions of the other four. After a concentrated review of the prerequisite mathematical background, Graph Algebras and Automata defines graph algebras and reveals their applicability to automata theory. It proceeds to explore assorted monoids, semigroups, rings, codes, and other algebraic structures and to outline theorems and algorithms for finite state automata and grammars.
Author : Saeed Salehi
Publisher : VDM Verlag Dr. Muller
Page : 35 pages
File Size : 30,69 MB
Release : 2010-02
Category :
ISBN : 3639230558
Trees are among the most fundamental and ubiquitous structures in mathematics and computer science. The notion of "tree" appears in many seemingly different areas from graph theory to universal algebra to logic. Tree languages and automata on trees have been studied extensively since the 1960s from both a purely mathematical and application point of view. Though the theory of tree automata and tree languages may have come into existence by generalizing string automata and languages, but it could not have stayed alive for long as a mere generalization. Apart from its intrinsic interest, this theory has found several applications and offers new perspectives to various parts of mathematical linguistics. It has been applied to the study of databases and XML schema languages, and provides tools for syntactic pattern recognition. When trees are defined as terms, universal algebra becomes directly applicable to tree automata and tree languages and, on the other hand, the theory of tree automata and tree languages suggests new notions and problems to universal algebra. In this book, the theory has been studied from the algebraic viewpoint.
Author : J. Richard Büchi
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 27,35 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 1461388538
The author, who died in 1984, is well-known both as a person and through his research in mathematical logic and theoretical computer science. In the first part of the book he presents the new classical theory of finite automata as unary algebras which he himself invented about 30 years ago. Many results, like his work on structure lattices or his characterization of regular sets by generalized regular rules, are unknown to a wider audience. In the second part of the book he extends the theory to general (non-unary, many-sorted) algebras, term rewriting systems, tree automata, and pushdown automata. Essentially Büchi worked independent of other rersearch, following a novel and stimulating approach. He aimed for a mathematical theory of terms, but could not finish the book. Many of the results are known by now, but to work further along this line presents a challenging research program on the borderline between universal algebra, term rewriting systems, and automata theory. For the whole book and again within each chapter the author starts at an elementary level, giving careful explanations and numerous examples and exercises, and then leads up to the research level. In this way he covers the basic theory as well as many nonstandard subjects. Thus the book serves as a textbook for both the beginner and the advances student, and also as a rich source for the expert.
Author : Jorge Almeida
Publisher : Springer Nature
Page : 278 pages
File Size : 11,96 MB
Release : 2020-09-10
Category : Mathematics
ISBN : 3030552152
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.
Author : Luca Aceto
Publisher : Springer Science & Business Media
Page : 751 pages
File Size : 27,35 MB
Release : 2008-06-24
Category : Computers
ISBN : 3540705821
ICALP 2008, the 35th edition of the International Colloquium on Automata, Languages and Programming, was held in Reykjavik, Iceland, July 7–11, 2008. ICALP is a series of annual conferences of the European Association for Th- reticalComputer Science(EATCS) which ?rsttook placein 1972.This year,the ICALP program consisted of the established Track A (focusing on algorithms, automata,complexityandgames)andTrackB(focusing onlogic,semanticsand theory of programming), and of the recently introduced Track C (focusing on security and cryptography foundations). In response to the call for papers, the Program Committees received 477 submissions, the highest ever: 269 for Track A, 122 for TrackB and 86 for Track C. Out of these, 126 papers were selected for inclusion in the scienti?c program: 70 papers for Track A, 32 for Track B and 24 for Track C. The selection was made by the Program Committees based on originality, quality, and relevance to theoretical computer science. The quality of the manuscripts was very high indeed, and many deserving papers could not be selected. ICALP 2008 consisted of ?ve invited lectures and the contributed papers.
Author : Boris Isaakovich Plotkin
Publisher : World Scientific
Page : 304 pages
File Size : 31,59 MB
Release : 1992
Category : Mathematics
ISBN : 9789810209360
The book is devoted to the investigation of algebraic structure. The emphasis is on the algebraic nature of real automation, which appears as a natural three-sorted algebraic structure, that allows for a rich algebraic theory. Based on a general category position, fuzzy and stochastic automata are defined. The final chapter is devoted to a database automata model. Database is defined as an algebraic structure and this allows us to consider theoretical problems of databases.