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Automata theory is the oldest among the disciplines constituting the subject matter of this Monograph Series: theoretical computer science. Indeed, automata theory and the closely related theory of formal languages form nowadays such a highly developed and diversified body of knowledge that even an exposition of "reasonably important" results is not possible within one volume. The purpose of this book is to develop the theory of automata and formal languages, starting from ideas based on linear algebra. By what was said above, it should be obvious that we do not intend to be encyclopedic. However, this book contains the basics of regular and context-free languages (including some new results), as well as a rather complete theory of pushdown automata and variations (e. g. counter automata). The wellknown AFL theory is extended to power series ("AFP theory"). Additional new results include, for instance, a grammatical characterization of the cones and the principal cones of context-free languages, as well as new decidability results.
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.
This work is an updated and considerably expanded version of the author's book The Theory of Semirings, with Applications to Mathematics and Theoretical Science, which has been recognized as the definitive reference work in this area. This edition includes many of the new results in this area, as well as further applications of semiring theory in such areas as idempotent analysis, discrete dynamical systems, formal language theory, fuzzy set theory, optimization etc. The book contains an extensive bibliography and a large number of examples. Audience: This book is aimed both at mathematicians and at researchers in applied mathematics and theoretical computer science. It is also suitable for use as a graduate-level textbook.
Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on solving this problem, and present many specific cases of applications. This book is essentially the third part of a trilogy, along with Semirings and their Applications, and Power Algebras over Semirings, both written by the same author and published by Kluwer Academic Publishers in 1999. While each book can be read independently of the others, to get the full force of the theory and applications one should have access to all three. This work will be of interest to academic and industrial researchers and graduate students. The intent of the book is to bring the applications to the attention of the abstract mathematicians and to make the abstract mathematics available to those who are using these tools in an ad-hoc manner without realizing the full force of the theory.
Annotation This book constitutes the refereed proceedings of the 32nd International Colloquium on Automata, Languages and Programming, ICALP 2005, held in Lisbon, Portugal in July 2005. The 113 revised full papers presented together with abstracts of 5 invited talks were carefully reviewed and selected from 407 submissions. The papers address all current issues in theoretical computer science and are organized in topical sections on data structures, cryptography and complexity, cryptography and distributed systems, graph algorithms, security mechanisms, automata and formal languages, signature and message authentication, algorithmic game theory, automata and logic, computational algebra, cache-oblivious algorithms and algorithmic engineering, on-line algorithms, security protocols logic, random graphs, concurrency, encryption and related primitives, approximation algorithms, games, lower bounds, probability, algebraic computation and communication complexity, string matching and computational biology, quantum complexity, analysis and verification, geometry and load balancing, concrete complexity and codes, and model theory and model checking.
This commemorative book celebrates the 70th birthday of Arto Kustaa Salomaa, one of the most influential researchers in theoretical computer science. The 24 invited papers by leading researchers in the area address a broad variety of topics in theoretical computer science and impressively reflect the breadth and the depth of Arto Salomaa's scientific work.
In subvolume 27C1 magnetic and related properties of binary lanthanide oxides have been compiled. This subvolume covers data obtained since 1980 and can therefore be regarded as supplement to volume III/12c. While in the previous volume the majority of magnetic data was obtained either from magnetometric measurements or from neutron diffraction, for the present data the main emphasis is devoted to 'related' properties without which, however, the understanding of classical magnetic properties is impossible. A second part 27C2 will deal with binary oxides of the actinide elements.
This book provides an introduction to the algebraic theory of semirings and, in this context, to basic algebraic concepts as e.g. semigroups, lattices and rings. It includes an algebraic theory of infinite sums as well as a detailed treatment of several applications in theoretical computer science. Complete proofs, various examples and exercises (some of them with solutions) make the book suitable for self-study. On the other hand, a more experienced reader who looks for information about the most common concepts and results on semirings will find cross-references throughout the book, a comprehensive bibliography and various hints to it.
The purpose of this book is to present an up to date account of fuzzy ideals of a semiring. The book concentrates on theoretical aspects and consists of eleven chapters including three invited chapters. Among the invited chapters, two are devoted to applications of Semirings to automata theory, and one deals with some generalizations of Semirings. This volume may serve as a useful hand book for graduate students and researchers in the areas of Mathematics and Theoretical Computer Science.
ICALP 2008, the 35th edition of the International Colloquium on Automata, Languages and Programming, was held in Reykjavik, Iceland, July 7–11, 2008. ICALP is a series of annual conferences of the European Association for Th- reticalComputer Science(EATCS) which ?rsttook placein 1972.This year,the ICALP program consisted of the established Track A (focusing on algorithms, automata,complexityandgames)andTrackB(focusing onlogic,semanticsand theory of programming), and of the recently introduced Track C (focusing on security and cryptography foundations). In response to the call for papers, the Program Committees received 477 submissions, the highest ever: 269 for Track A, 122 for TrackB and 86 for Track C. Out of these, 126 papers were selected for inclusion in the scienti?c program: 70 papers for Track A, 32 for Track B and 24 for Track C. The selection was made by the Program Committees based on originality, quality, and relevance to theoretical computer science. The quality of the manuscripts was very high indeed, and many deserving papers could not be selected. ICALP 2008 consisted of ?ve invited lectures and the contributed papers.