Automata Theory and its Applications


Author: Bakhadyr Khoussainov,Anil Nerode
Publisher: Springer Science & Business Media
ISBN: 1461201713
Category: Mathematics
Page: 432
View: 4132

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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.

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: 3227

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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.

Cryptographic Applications of Analytic Number Theory

Complexity Lower Bounds and Pseudorandomness
Author: Igor Shparlinski
Publisher: Birkhäuser
ISBN: 3034880375
Category: Mathematics
Page: 414
View: 9859

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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.

Formal Languages, Automata and Numeration Systems 2

Applications to Recognizability and Decidability
Author: Michel Rigo
Publisher: John Wiley & Sons
ISBN: 1119042860
Category: Technology & Engineering
Page: 246
View: 6046

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The interplay between words, computability, algebra andarithmetic has now proved its relevance and fruitfulness. Indeed,the cross-fertilization between formal logic and finite automata(such as that initiated by J.R. Büchi) or betweencombinatorics on words and number theory has paved the way torecent dramatic developments, for example, the transcendenceresults for the real numbers having a “simple” binaryexpansion, by B. Adamczewski and Y. Bugeaud. This book is at the heart of this interplay through a unifiedexposition. Objects are considered with a perspective that comesboth from theoretical computer science and mathematics. Theoreticalcomputer science offers here topics such as decision problems andrecognizability issues, whereas mathematics offers concepts such asdiscrete dynamical systems. The main goal is to give a quick access, for students andresearchers in mathematics or computer science, to actual researchtopics at the intersection between automata and formal languagetheory, number theory and combinatorics on words. The second of two volumes on this subject, this book coversregular languages, numeration systems, formal methods applied todecidability issues about infinite words and sets of numbers.

Formal Languages, Automata and Numeration Systems 1

Introduction to Combinatorics on Words
Author: Michel Rigo
Publisher: John Wiley & Sons
ISBN: 1119008220
Category: Computers
Page: 338
View: 4925

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Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidable regularities or patterns. When considering some numeration systems, any integer can be represented as a finite word over an alphabet of digits. This simple observation leads to the study of the relationship between the arithmetical properties of the integers and the syntactical properties of the corresponding representations. One of the most profound results in this direction is given by the celebrated theorem by Cobham. Surprisingly, a recent extension of this result to complex numbers led to the famous Four Exponentials Conjecture. This is just one example of the fruitful relationship between formal language theory (including the theory of automata) and number theory.

Theoretical Advances and Applications of Fuzzy Logic and Soft Computing


Author: Oscar Castillo,Patricia Melin,Oscar Montiel Ross,Roberto Sepúlveda Cruz,Witold Pedrycz
Publisher: Springer Science & Business Media
ISBN: 3540724346
Category: Mathematics
Page: 626
View: 5242

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This book comprises a selection of papers on theoretical advances and applications of fuzzy logic and soft computing from the IFSA 2007 World Congress, held in Cancun, Mexico, June 2007. These papers constitute an important contribution to the theory and applications of fuzzy logic and soft computing methodologies.

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: 9216

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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.

CONCUR '94, Concurrency Theory

5th International Conference, Uppsala, Sweden, August 22-25, 1994 : Proceedings
Author: Bengt Jonsson,Joachim Parrow
Publisher: Springer
ISBN: N.A
Category: Computer programs
Page: 528
View: 4957

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"This volume constitutes the proceedings of the Fifth International Conference on Concurrency Theory, CONCUR '94, held at Uppsala, Sweden in August 1994. In total, 29 refereed research papers selected from 108 submissions for the conference are presented together with full papers or abstracts of the 5 invited talks by prominent speakers. The book contains recent results on all relevant aspects of concurrency research and thus competently documents the progress of the field since the predecessor conference CONCUR '93, the proceedings of which are published as LNCS 715"--PUBLISHER'S WEBSITE.

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: 2640

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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.

Evolutionary Systems

Biological and Epistemological Perspectives on Selection and Self-Organization
Author: G. Vijver,Stanley N. Salthe,M. Delpos
Publisher: Springer Science & Business Media
ISBN: 9401715106
Category: Philosophy
Page: 438
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The three well known revolutions of the past centuries - the Copernican, the Darwinian and the Freudian - each in their own way had a deflating and mechanizing effect on the position of humans in nature. They opened up a richness of disillusion: earth acquired a more modest place in the universe, the human body and mind became products of a long material evolutionary history, and human reason, instead of being the central, immaterial, locus of understanding, was admitted into the theater of discourse only as a materialized and frequently out-of-control actor. Is there something objectionable to this picture? Formulated as such, probably not. Why should we resist the idea that we are in certain ways, and to some degree, physically, biologically or psychically determined? Why refuse to acknowledge the fact that we are materially situated in an ever evolving world? Why deny that the ways of inscription (traces of past events and processes) are co-determinative of further "evolutionary pathways"? Why minimize the idea that each intervention, of each natural being, is temporally and materially situated, and has, as such, the inevitable consequence of changing the world? The point is, however, that there are many, more or less radically different, ways to consider the "mechanization" of man and nature. There are, in particular, many ways to get the message of "material and evolutionary determination", as well as many levels at which this determination can be thought of as relevant or irrelevant.

Handbook of Model Checking


Author: Edmund M. Clarke,Thomas A. Henzinger,Helmut Veith,Roderick Bloem
Publisher: Springer
ISBN: 3319105752
Category: Computers
Page: 1210
View: 7192

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Model checking is a computer-assisted method for the analysis of dynamical systems that can be modeled by state-transition systems. Drawing from research traditions in mathematical logic, programming languages, hardware design, and theoretical computer science, model checking is now widely used for the verification of hardware and software in industry. The editors and authors of this handbook are among the world's leading researchers in this domain, and the 32 contributed chapters present a thorough view of the origin, theory, and application of model checking. In particular, the editors classify the advances in this domain and the chapters of the handbook in terms of two recurrent themes that have driven much of the research agenda: the algorithmic challenge, that is, designing model-checking algorithms that scale to real-life problems; and the modeling challenge, that is, extending the formalism beyond Kripke structures and temporal logic. The book will be valuable for researchers and graduate students engaged with the development of formal methods and verification tools.

Advances in Temporal Logic


Author: Howard Barringer,Michael Fisher,Dov M. Gabbay,Graham Gough
Publisher: Springer Science & Business Media
ISBN: 9401595860
Category: Mathematics
Page: 453
View: 3898

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Time is a fascinating subject and has long since captured mankind's imagination, from the ancients to modern man, both adult and child alike. It has been studied across a wide range of disciplines, from the natural sciences to philosophy and logic. Today, thirty plus years since Prior's work in laying out foundations for temporal logic, and two decades on from Pnueli's seminal work applying of temporal logic in specification and verification of computer programs, temporal logic has a strong and thriving international research community within the broad disciplines of computer science and artificial intelligence. Areas of activity include, but are certainly not restricted to: Pure Temporal Logic, e. g. temporal systems, proof theory, model theory, expressiveness and complexity issues, algebraic properties, application of game theory; Specification and Verification, e. g. of reactive systems, ofreal-time components, of user interaction, of hardware systems, techniques and tools for verification, execution and prototyping methods; Temporal Databases, e. g. temporal representation, temporal query ing, granularity of time, update mechanisms, active temporal data bases, hypothetical reasoning; Temporal Aspects in AI, e. g. modelling temporal phenomena, in terval temporal calculi, temporal nonmonotonicity, interaction of temporal reasoning with action/knowledge/belief logics, temporal planning; Tense and Aspect in Natural Language, e. g. models, ontologies, temporal quantifiers, connectives, prepositions, processing tempo ral statements; Temporal Theorem Proving, e. g. translation methods, clausal and non-clausal resolution, tableaux, automata-theoretic approaches, tools and practical systems.