Fault tolerance has been an active research area for many years. This volume presents papers from a workshop held in 1993 where a small number of key researchers and practitioners in the area met to discuss the experiences of industrial practitioners, to provide a perspective on the state of the art of fault tolerance research, to determine whether the subject is becoming mature, and to learn from the experiences so far in order to identify what might be important research topics for the coming years. The workshop provided a more intimate environment for discussions and presentations than usual at conferences. The papers in the volume were presented at the workshop, then updated and revised to reflect what was learned at the workshop.
This volume is the proceedings of the first International Workshop on Orders, Algorithms, and Applications, held at Lyon, France in July 1994. Ordered sets and the more specifically algorithmic aspects of order theory are of increasing importance, for example in graph theory. They enjoy a recognized place in computer science as well as in mathematics, due to various new developments in the last few years. The nine technical papers accepted for this volume and the four invited papers presented offer a representative perspective on theoretical and applicational aspects of orders and related algorithms.
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.
Advanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of the book covers basic material related to linear recurrence relations with application to counting and the asymptotic estimate of the rate of growth of a sequence satisfying a recurrence relation.
The interplay between words, computability, algebra and arithmetic 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 between combinatorics on words and number theory has paved the way to recent dramatic developments, for example, the transcendence results for the real numbers having a "simple" binary expansion, by B. Adamczewski and Y. Bugeaud. This book is at the heart of this interplay through a unified exposition. Objects are considered with a perspective that comes both from theoretical computer science and mathematics. Theoretical computer science offers here topics such as decision problems and recognizability issues, whereas mathematics offers concepts such as discrete dynamical systems. The main goal is to give a quick access, for students and researchers in mathematics or computer science, to actual research topics at the intersection between automata and formal language theory, number theory and combinatorics on words. The second of two volumes on this subject, this book covers regular languages, numeration systems, formal methods applied to decidability issues about infinite words and sets of numbers.
Fault tolerance has been an active research area for many years. This volume presents papers from a workshop held in 1993 where a small number of key researchers and practitioners in the area met to discuss the experiences of industrial practitioners, to provide a perspective on the state of the art of fault tolerance research, to determine whether the subject is becoming mature, and to learn from the experiences so far in order to identify what might be important research topics for the coming years. The workshop provided a more intimate environment for discussions and presentations than usual at conferences. The papers in the volume were presented at the workshop, then updated and revised to reflect what was learned at the workshop.
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