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Products of Automata

2012-12-06 Computers
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Release : 2012-12-06
Genre : Computers
Kind : eBook
Book Rating : 119/5 ( reviews)

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Book Synopsis Products of Automata by : Ferenc Gecseg

Download or read book Products of Automata written by Ferenc Gecseg. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Weighted Automata

2009-09-18 Computers
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Release : 2009-09-18
Genre : Computers
Kind : eBook
Book Rating : 925/5 ( reviews)

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Book Synopsis Handbook of Weighted Automata by : Manfred Droste

Download or read book Handbook of Weighted Automata written by Manfred Droste. This book was released on 2009-09-18. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elements of Automata Theory

2009-10-01 Mathematics
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Release : 2009-10-01
Genre : Mathematics
Kind : eBook
Book Rating : 797/5 ( reviews)

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Book Synopsis Elements of Automata Theory by : Jacques Sakarovitch

Download or read book Elements of Automata Theory written by Jacques Sakarovitch. This book was released on 2009-10-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Theory of Automata Networks

2005-01-01 Mathematics
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Release : 2005-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 492/5 ( reviews)

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Book Synopsis Algebraic Theory of Automata Networks by : Pal Domosi

Download or read book Algebraic Theory of Automata Networks written by Pal Domosi. This book was released on 2005-01-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Cellular Automata Machines

1987 Computers
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Release : 1987
Genre : Computers
Kind : eBook
Book Rating : 608/5 ( reviews)

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Book Synopsis Cellular Automata Machines by : Tommaso Toffoli

Download or read book Cellular Automata Machines written by Tommaso Toffoli. This book was released on 1987. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Computation -- Computation by Abstracts Devices.

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