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Author: Ferenc Gecseg
Publisher: Springer Science & Business Media
ISBN: 3642616119
Category : Computers
Languages : en
Pages : 114
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Book Description
Both theoretical and practical considerations motivate the repre sentation of objects as certain compositions of simpler ones. In the theory of automata this observation has led to the concepts of pro ducts and complete systems of automata. In the general form of the products of automata all the component automata are fed back to one another. With this very broad notion of products, the realization of automata with large numbers of states by means of compositions of basic components is a highly involved process; this increases the possibility of errors. In order to decrease the complexity of feedbacks, a hierarchy of products called lXi-pro ducts was introduced some 10 years ago, where i runs over the set of all non-negative integers. In an IXcproduct the index set of the component automata is linearly ordered. The input of each automaton in the product may depend on the states of all automata preceding it, i. e. , all component automata steer all those automata which follow them in the product. Furthermore, at most the next i-I automata (including itself) may be fed back to the input of a given component automaton. Thus for iXcproducts the lengths of feedbacks are at most i. The aim of this monograph is to give a systematic account of iXi-Products. It consists of five chapters, a reference section, and an index. The first chapter contains the necessary concepts and results from universal algebra, automata, and sequential machines.
Author: Ferenc Gecseg
Publisher: Springer Science & Business Media
ISBN: 3642616119
Category : Computers
Languages : en
Pages : 114
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Book Description
Both theoretical and practical considerations motivate the repre sentation of objects as certain compositions of simpler ones. In the theory of automata this observation has led to the concepts of pro ducts and complete systems of automata. In the general form of the products of automata all the component automata are fed back to one another. With this very broad notion of products, the realization of automata with large numbers of states by means of compositions of basic components is a highly involved process; this increases the possibility of errors. In order to decrease the complexity of feedbacks, a hierarchy of products called lXi-pro ducts was introduced some 10 years ago, where i runs over the set of all non-negative integers. In an IXcproduct the index set of the component automata is linearly ordered. The input of each automaton in the product may depend on the states of all automata preceding it, i. e. , all component automata steer all those automata which follow them in the product. Furthermore, at most the next i-I automata (including itself) may be fed back to the input of a given component automaton. Thus for iXcproducts the lengths of feedbacks are at most i. The aim of this monograph is to give a systematic account of iXi-Products. It consists of five chapters, a reference section, and an index. The first chapter contains the necessary concepts and results from universal algebra, automata, and sequential machines.
Author: Manfred Droste
Publisher: Springer Science & Business Media
ISBN: 3642014925
Category : Computers
Languages : en
Pages : 614
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Book Description
The purpose of this Handbook is to highlight both theory and applications of weighted automata. Weighted finite automata are classical nondeterministic finite automata in which the transitions carry weights. These weights may model, e. g. , the cost involved when executing a transition, the amount of resources or time needed for this,or the probability or reliability of its successful execution. The behavior of weighted finite automata can then be considered as the function (suitably defined) associating with each word the weight of its execution. Clearly, weights can also be added to classical automata with infinite state sets like pushdown automata; this extension constitutes the general concept of weighted automata. To illustrate the diversity of weighted automata, let us consider the following scenarios. Assume that a quantitative system is modeled by a classical automaton in which the transitions carry as weights the amount of resources needed for their execution. Then the amount of resources needed for a path in this weighted automaton is obtained simply as the sum of the weights of its transitions. Given a word, we might be interested in the minimal amount of resources needed for its execution, i. e. , for the successful paths realizing the given word. In this example, we could also replace the “resources” by “profit” and then be interested in the maximal profit realized, correspondingly, by a given word.
Author: Jacques Sakarovitch
Publisher: Cambridge University Press
ISBN: 1139643797
Category : Mathematics
Languages : en
Pages : 818
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Book Description
Automata theory lies at the foundation of computer science, and is vital to a theoretical understanding of how computers work and what constitutes formal methods. This treatise gives a rigorous account of the topic and illuminates its real meaning by looking at the subject in a variety of ways. The first part of the book is organised around notions of rationality and recognisability. The second part deals with relations between words realised by finite automata, which not only exemplifies the automata theory but also illustrates the variety of its methods and its fields of application. Many exercises are included, ranging from those that test the reader, to those that are technical results, to those that extend ideas presented in the text. Solutions or answers to many of these are included in the book.
Author: Pal Domosi
Publisher: SIAM
ISBN: 9780898718492
Category : Mathematics
Languages : en
Pages : 270
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Book Description
Investigates automata networks as algebraic structures and develops their theory in line with other algebraic theories, such as those of semigroups, groups, rings, and fields. The authors also investigate automata networks as products of automata, that is, as compositions of automata obtained by cascading without feedback or with feedback of various restricted types or, most generally, with the feedback dependencies controlled by an arbitrary directed graph. They survey and extend the fundamental results in regard to automata networks, including the main decomposition theorems of Letichevsky, of Krohn and Rhodes, and of others.
Author: Kumpati S. Narendra
Publisher: Courier Corporation
ISBN: 0486268462
Category : Technology & Engineering
Languages : en
Pages : 498
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Book Description
This self-contained introductory text on the behavior of learning automata focuses on how a sequential decision-maker with a finite number of choices responds in a random environment. Topics include fixed structure automata, variable structure stochastic automata, convergence, 0 and S models, nonstationary environments, interconnected automata and games, and applications of learning automata. A must for all students of stochastic algorithms, this treatment is the work of two well-known scientists and is suitable for a one-semester graduate course in automata theory and stochastic algorithms. This volume also provides a fine guide for independent study and a reference for students and professionals in operations research, computer science, artificial intelligence, and robotics. The authors have provided a new preface for this edition.
Author: Ding-Zhu Du
Publisher: John Wiley & Sons
ISBN: 0471464082
Category : Computers
Languages : en
Pages : 405
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Book Description
Automata and natural language theory are topics lying at the heart of computer science. Both are linked to computational complexity and together, these disciplines help define the parameters of what constitutes a computer, the structure of programs, which problems are solvable by computers, and a range of other crucial aspects of the practice of computer science. In this important volume, two respected authors/editors in the field offer accessible, practice-oriented coverage of these issues with an emphasis on refining core problem solving skills.
Author: Jean Berstel
Publisher: Cambridge University Press
ISBN: 052188831X
Category : Computers
Languages : en
Pages : 634
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Book Description
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.
Author: Howard Straubing
Publisher: Springer Science & Business Media
ISBN: 1461202892
Category : Computers
Languages : en
Pages : 235
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Book Description
The study of the connections between mathematical automata and for mal logic is as old as theoretical computer science itself. In the founding paper of the subject, published in 1936, Turing showed how to describe the behavior of a universal computing machine with a formula of first order predicate logic, and thereby concluded that there is no algorithm for deciding the validity of sentences in this logic. Research on the log ical aspects of the theory of finite-state automata, which is the subject of this book, began in the early 1960's with the work of J. Richard Biichi on monadic second-order logic. Biichi's investigations were extended in several directions. One of these, explored by McNaughton and Papert in their 1971 monograph Counter-free Automata, was the characterization of automata that admit first-order behavioral descriptions, in terms of the semigroup theoretic approach to automata that had recently been developed in the work of Krohn and Rhodes and of Schiitzenberger. In the more than twenty years that have passed since the appearance of McNaughton and Papert's book, the underlying semigroup theory has grown enor mously, permitting a considerable extension of their results. During the same period, however, fundamental investigations in the theory of finite automata by and large fell out of fashion in the theoretical com puter science community, which moved to other concerns.
Author: Dexter C. Kozen
Publisher: Springer
ISBN: 364285706X
Category : Computers
Languages : en
Pages : 399
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Book Description
These are my lecture notes from CS381/481: Automata and Computability Theory, a one-semester senior-level course I have taught at Cornell Uni versity for many years. I took this course myself in thc fall of 1974 as a first-year Ph.D. student at Cornell from Juris Hartmanis and have been in love with the subject ever sin,:e. The course is required for computer science majors at Cornell. It exists in two forms: CS481, an honors version; and CS381, a somewhat gentler paced version. The syllabus is roughly the same, but CS481 go es deeper into thc subject, covers more material, and is taught at a more abstract level. Students are encouraged to start off in one or the other, then switch within the first few weeks if they find the other version more suitaLle to their level of mathematical skill. The purpose of t.hc course is twofold: to introduce computer science students to the rieh heritage of models and abstractions that have arisen over the years; and to dew!c'p the capacity to form abstractions of their own and reason in terms of them.
Author: John Carroll
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 456
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Book Description
