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Computer Science - Theory and Applications
This book features the refereed proceedings of the 2nd International Symposium on Computer Science in Russia held in September 2007. The 35 papers cover theory track deals with algorithms, protocols, and data structures; complexity and cryptography; formal languages, automata and their applications to computer science; computational models and concepts; proof theory; and applications of logic to computer science. Many applications are presented.
Handbook of Formal Languages
This third volume of the Handbook of Formal Languages discusses language theory beyond linear or string models: trees, graphs, grids, pictures, computer graphics. Many chapters offer an authoritative self-contained exposition of an entire area. Special emphasis is on interconnections with logic.
Developments in Language Theory
This book constitutes the proceedings of the 13th International Conference, DLT 2009, held in Stuttgart, Germany from June 30 until July 3, 2009. The 35 papers presented together with 4 invited talks were carefully reviewed and selected from 70 submissions. The papers presented address topics on formal languages, automata theory, computability, complexity, logic, petri nets and related areas.
Computational and Combinatorial Group Theory and Cryptography
This volume contains the proceedings of the AMS Special Session on Computational Algebra, Groups, and Applications, held April 30-May 1, 2011, at the University of Nevada, Las Vegas, Nevada, and the AMS Special Session on the Mathematical Aspects of Cryptography and Cyber Security, held September 10-11, 2011, at Cornell University, Ithaca, New York. Over the past twenty years combinatorial and infinite group theory has been energized by three developments: the emergence of geometric and asymptotic group theory, the development of algebraic geometry over groups leading to the solution of the Tarski problems, and the development of group-based cryptography. These three areas in turn have had an impact on computational algebra and complexity theory. The papers in this volume, both survey and research, exhibit the tremendous vitality that is at the heart of group theory in the beginning of the twenty-first century as well as the diversity of interests in the field.
Algorithms Unplugged
Algorithms specify the way computers process information and how they execute tasks. Many recent technological innovations and achievements rely on algorithmic ideas – they facilitate new applications in science, medicine, production, logistics, traffic, communi¬cation and entertainment. Efficient algorithms not only enable your personal computer to execute the newest generation of games with features unimaginable only a few years ago, they are also key to several recent scientific breakthroughs – for example, the sequencing of the human genome would not have been possible without the invention of new algorithmic ideas that speed up computations by several orders of magnitude. The great...
Abstract Algebra
Abstract algebra is the study of algebraic structures like groups, rings and fields. This book provides an account of the theoretical foundations including applications to Galois Theory, Algebraic Geometry and Representation Theory. It implements the pedagogic approach to conveying algebra from the perspective of rings. The 3rd edition provides a revised and extended versions of the chapters on Algebraic Cryptography and Geometric Group Theory.
Finitely Presented Groups
This book contains surveys and research articles on the state-of-the-art in finitely presented groups for researchers and graduate students. Overviews of current trends in exponential groups and of the classification of finite triangle groups and finite generalized tetrahedron groups are complemented by new results on a conjecture of Rosenberger and an approximation theorem. A special emphasis is on algorithmic techniques and their complexity, both for finitely generated groups and for finite Z-algebras, including explicit computer calculations highlighting important classical methods. A further chapter surveys connections to mathematical logic, in particular to universal theories of various classes of groups, and contains new results on countable elementary free groups. Applications to cryptography include overviews of techniques based on representations of p-groups and of non-commutative group actions. Further applications of finitely generated groups to topology and artificial intelligence complete the volume. All in all, leading experts provide up-to-date overviews and current trends in combinatorial group theory and its connections to cryptography and other areas.
Developments in Language Theory
This book constitutes the refereed proceedings of the 10th International Conference on Developments in Language Theory, DLT 2006, held in Santa Barbara, CA, June 2006. The book presents 36 revised full papers together with 4 invited papers. All important issues in language theory are addressed including grammars, acceptors and transducers for strings, trees, graphs, arrays; efficient text algorithms; algebraic theories for automata and languages; and more.
Languages and Automata
This reference discusses how automata and language theory can be used to understand solutions to solving equations in groups and word problems in groups. Examples presented include, how Fine scale complexity theory has entered group theory via these connections and how cellular automata, has been generalized into a group theoretic setting. Chapters written by experts in group theory and computer science explain these connections.
