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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: Pal Domosi
Publisher: SIAM
ISBN: 9780898718492
Category : Mathematics
Languages : en
Pages : 270
Get Book Here
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: E. Goles
Publisher: Springer Science & Business Media
ISBN: 9400905297
Category : Computers
Languages : en
Pages : 259
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Book Description
"Et moi ..., si j'avait Sll comment en revenir. One sennce mathematics has rendered the human race. It has put common sense back je n'y serais point alle.' Jules Verne whe", it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be smse'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'!ltre of this series
Author: M.A.L. Thathachar
Publisher: Springer Science & Business Media
ISBN: 1441990526
Category : Science
Languages : en
Pages : 275
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Book Description
Networks of Learning Automata: Techniques for Online Stochastic Optimization is a comprehensive account of learning automata models with emphasis on multiautomata systems. It considers synthesis of complex learning structures from simple building blocks and uses stochastic algorithms for refining probabilities of selecting actions. Mathematical analysis of the behavior of games and feedforward networks is provided. Algorithms considered here can be used for online optimization of systems based on noisy measurements of performance index. Also, algorithms that assure convergence to the global optimum are presented. Parallel operation of automata systems for improving speed of convergence is described. The authors also include extensive discussion of how learning automata solutions can be constructed in a variety of applications.
Author: Juraj Hromkovič
Publisher: Springer Science & Business Media
ISBN: 9783540140153
Category : Computers
Languages : en
Pages : 336
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Book Description
Juraj Hromkovic takes the reader on an elegant route through the theoretical fundamentals of computer science. The author shows that theoretical computer science is a fascinating discipline, full of spectacular contributions and miracles. The book also presents the development of the computer scientist's way of thinking as well as fundamental concepts such as approximation and randomization in algorithmics, and the basic ideas of cryptography and interconnection network design.
Author: Max Garzon
Publisher: Springer Science & Business Media
ISBN: 3642779050
Category : Computers
Languages : en
Pages : 284
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Book Description
Locality is a fundamental restriction in nature. On the other hand, adaptive complex systems, life in particular, exhibit a sense of permanence and time lessness amidst relentless constant changes in surrounding environments that make the global properties of the physical world the most important problems in understanding their nature and structure. Thus, much of the differential and integral Calculus deals with the problem of passing from local information (as expressed, for example, by a differential equation, or the contour of a region) to global features of a system's behavior (an equation of growth, or an area). Fundamental laws in the exact sciences seek to express the observable global behavior of physical objects through equations about local interaction of their components, on the assumption that the continuum is the most accurate model of physical reality. Paradoxically, much of modern physics calls for a fundamen tal discrete component in our understanding of the physical world. Useful computational models must be eventually constructed in hardware, and as such can only be based on local interaction of simple processing elements.
Author: Françoise Fogelman Soulié
Publisher: Manchester University Press
ISBN: 9780719022098
Category : Computers
Languages : en
Pages : 304
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Book Description
Author: Alireza Rezvanian
Publisher: Springer
ISBN: 3319724282
Category : Technology & Engineering
Languages : en
Pages : 471
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Book Description
This book collects recent theoretical advances and concrete applications of learning automata (LAs) in various areas of computer science, presenting a broad treatment of the computer science field in a survey style. Learning automata (LAs) have proven to be effective decision-making agents, especially within unknown stochastic environments. The book starts with a brief explanation of LAs and their baseline variations. It subsequently introduces readers to a number of recently developed, complex structures used to supplement LAs, and describes their steady-state behaviors. These complex structures have been developed because, by design, LAs are simple units used to perform simple tasks; their full potential can only be tapped when several interconnected LAs cooperate to produce a group synergy. In turn, the next part of the book highlights a range of LA-based applications in diverse computer science domains, from wireless sensor networks, to peer-to-peer networks, to complex social networks, and finally to Petri nets. The book accompanies the reader on a comprehensive journey, starting from basic concepts, continuing to recent theoretical findings, and ending in the applications of LAs in problems from numerous research domains. As such, the book offers a valuable resource for all computer engineers, scientists, and students, especially those whose work involves the reinforcement learning and artificial intelligence domains.
Author: Gerard Weisbuch
Publisher: CRC Press
ISBN: 0429717563
Category : Mathematics
Languages : en
Pages : 209
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Book Description
This book provides an accessible introduction to complex systems viewed as networks of automata, using primarily examples drawn from the physics of disordered systems, neural networks, and the origins of life. It is helpful for readers with a university education in science or engineering.
Author: Sergey Ablameyko
Publisher: IOS Press
ISBN: 9781586033248
Category : Electronic books
Languages : en
Pages : 262
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Book Description
This work reports critical analyses on complexity issues in the continuum setting and on generalization to new examples, which are two basic milestones in learning from examples in connectionist models. It also covers up-to-date developments in computational mathematics.
Author: Paul Smolensky
Publisher: Psychology Press
ISBN: 1134773013
Category : Psychology
Languages : en
Pages : 890
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Book Description
Recent years have seen an explosion of new mathematical results on learning and processing in neural networks. This body of results rests on a breadth of mathematical background which even few specialists possess. In a format intermediate between a textbook and a collection of research articles, this book has been assembled to present a sample of these results, and to fill in the necessary background, in such areas as computability theory, computational complexity theory, the theory of analog computation, stochastic processes, dynamical systems, control theory, time-series analysis, Bayesian analysis, regularization theory, information theory, computational learning theory, and mathematical statistics. Mathematical models of neural networks display an amazing richness and diversity. Neural networks can be formally modeled as computational systems, as physical or dynamical systems, and as statistical analyzers. Within each of these three broad perspectives, there are a number of particular approaches. For each of 16 particular mathematical perspectives on neural networks, the contributing authors provide introductions to the background mathematics, and address questions such as: * Exactly what mathematical systems are used to model neural networks from the given perspective? * What formal questions about neural networks can then be addressed? * What are typical results that can be obtained? and * What are the outstanding open problems? A distinctive feature of this volume is that for each perspective presented in one of the contributed chapters, the first editor has provided a moderately detailed summary of the formal results and the requisite mathematical concepts. These summaries are presented in four chapters that tie together the 16 contributed chapters: three develop a coherent view of the three general perspectives -- computational, dynamical, and statistical; the other assembles these three perspectives into a unified overview of the neural networks field.
