Automata Theory and its Applications

Author: Bakhadyr Khoussainov,Anil Nerode

Publisher: Springer Science & Business Media

ISBN: 1461201713

Category: Mathematics

Page: 432

View: 9606

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The theory of finite automata on finite stings, infinite strings, and trees has had a dis tinguished history. First, automata were introduced to represent idealized switching circuits augmented by unit delays. This was the period of Shannon, McCullouch and Pitts, and Howard Aiken, ending about 1950. Then in the 1950s there was the work of Kleene on representable events, of Myhill and Nerode on finite coset congruence relations on strings, of Rabin and Scott on power set automata. In the 1960s, there was the work of Btichi on automata on infinite strings and the second order theory of one successor, then Rabin's 1968 result on automata on infinite trees and the second order theory of two successors. The latter was a mystery until the introduction of forgetful determinacy games by Gurevich and Harrington in 1982. Each of these developments has successful and prospective applications in computer science. They should all be part of every computer scientist's toolbox. Suppose that we take a computer scientist's point of view. One can think of finite automata as the mathematical representation of programs that run us ing fixed finite resources. Then Btichi's SIS can be thought of as a theory of programs which run forever (like operating systems or banking systems) and are deterministic. Finally, Rabin's S2S is a theory of programs which run forever and are nondeterministic. Indeed many questions of verification can be decided in the decidable theories of these automata.
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Automata, Logics, and Infinite Games

A Guide to Current Research

Author: Erich Grädel,Wolfgang Thomas,Thomas Wilke

Publisher: Springer

ISBN: 3540363874

Category: Computers

Page: 392

View: 5115

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A central aim and ever-lasting dream of computer science is to put the development of hardware and software systems on a mathematical basis which is both firm and practical. Such a scientific foundation is needed especially for the construction of reactive programs, like communication protocols or control systems. For the construction and analysis of reactive systems an elegant and powerful theory has been developed based on automata theory, logical systems for the specification of nonterminating behavior, and infinite two-person games. The 19 chapters presented in this multi-author monograph give a consolidated overview of the research results achieved in the theory of automata, logics, and infinite games during the past 10 years. Special emphasis is placed on coherent style, complete coverage of all relevant topics, motivation, examples, justification of constructions, and exercises.
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Cryptographic Applications of Analytic Number Theory

Complexity Lower Bounds and Pseudorandomness

Author: Igor Shparlinski

Publisher: Birkhäuser

ISBN: 3034880375

Category: Mathematics

Page: 414

View: 1437

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The book introduces new techniques that imply rigorous lower bounds on the com plexity of some number-theoretic and cryptographic problems. It also establishes certain attractive pseudorandom properties of various cryptographic primitives. These methods and techniques are based on bounds of character sums and num bers of solutions of some polynomial equations over finite fields and residue rings. Other number theoretic techniques such as sieve methods and lattice reduction algorithms are used as well. The book also contains a number of open problems and proposals for further research. The emphasis is on obtaining unconditional rigorously proved statements. The bright side of this approach is that the results do not depend on any assumptions or conjectures. On the downside, the results are much weaker than those which are widely believed to be true. We obtain several lower bounds, exponential in terms of logp, on the degrees and orders of o polynomials; o algebraic functions; o Boolean functions; o linear recurrence sequences; coinciding with values of the discrete logarithm modulo a prime p at sufficiently many points (the number of points can be as small as pI/2+O:). These functions are considered over the residue ring modulo p and over the residue ring modulo an arbitrary divisor d of p - 1. The case of d = 2 is of special interest since it corresponds to the representation of the rightmost bit of the discrete logarithm and defines whether the argument is a quadratic residue.
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Fuzzy Logic in Action: Applications in Epidemiology and Beyond

Author: Eduardo Massad,Neli Regina Siqueira Ortega,Laecio Carvalho de Barros,Claudio J. Struchiner

Publisher: Springer Science & Business Media

ISBN: 3540690921

Category: Medical

Page: 347

View: 3541

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Fuzzy Logic in Action: Applications in Epidemiology and Beyond, co-authored by Eduardo Massad, Neli Ortega, Laécio Barros, and Cláudio Struchiner is a remarkable achievement. The book brings a major paradigm shift to medical sciences exploring the use of fuzzy sets in epidemiology and medical diagnosis arena. The volume addresses the most significant topics in the broad areas of epidemiology, mathematical modeling and uncertainty, embodying them within the framework of fuzzy set and dynamic systems theory. Written by leading contributors to the area of epidemiology, medical informatics and mathematics, the book combines a very lucid and authoritative exposition of the fundamentals of fuzzy sets with an insightful use of the fundamentals in the area of epidemiology and diagnosis. The content is clearly illustrated by numerous illustrative examples and several real world applications. Based on their profound knowledge of epidemiology and mathematical modeling, and on their keen understanding of the role played by uncertainty and fuzzy sets, the authors provide insights into the connections between biological phenomena and dynamic systems as a mean to predict, diagnose, and prescribe actions. An example is the use of Bellman-Zadeh fuzzy decision making approach to develop a vaccination strategy to manage measles epidemics in São Paulo. The book offers a comprehensive, systematic, fully updated and self- contained treatise of fuzzy sets in epidemiology and diagnosis. Its content covers material of vital interest to students, researchers and practitioners and is suitable both as a textbook and as a reference. The authors present new results of their own in most of the chapters. In doing so, they reflect the trend to view fuzzy sets, probability theory and statistics as an association of complementary and synergetic modeling methodologies.
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Advances in Computer Science and its Applications

CSA 2013

Author: Hwa Young Jeong,Mohammad S. Obaidat,Neil Y. Yen,James J. (Jong Hyuk) Park

Publisher: Springer Science & Business Media

ISBN: 3642416748

Category: Mathematics

Page: 749

View: 3913

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These proceedings focus on various aspects of computer science and its applications, thus providing an opportunity for academic and industry professionals to discuss the latest issues and progress in this and related areas. The book includes theory and applications alike.
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AI 2001: Advances in Artificial Intelligence

14th International Joint Conference on Artificial Intelligence, Adelaide, Australia, December 10-14, 2001, Proceedings

Author: Mike Brooks,Dan Corbett,Markus Stumptner

Publisher: Springer

ISBN: N.A

Category: Artificial intelligence

Page: 666

View: 5897

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This book constitutes the refereed proceedings of the 14th Australian Joint Conference on Artificial Intelligence, AI 2001, held in Adelaide, Australia, in December 2001. The 55 revised full papers presented together with one invited contribution were carefully reviewed and selected from a total of 100 submissions. The papers cover the whole range of artificial intelligence from theoretical and foundational issues to advanced applications in a variety of fields.
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