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Die Grundidee des vorliegenden Lehrbuchs ist, wesentliche Elemente der diskreten Mathematik zu vermitteln, um die modernen Entwicklungen im Informationszeitalter kompetent mathematisch beurteilen zu konnen. Hierzu gehort das Verstandnis von Graphen, das Rechnen mit grossen Zahlen und das Rechnen modulo n. Die Autoren beginnen mit einer Darstellung der elementaren Zahlentheorie. Insbesondere wird die Verschlusselung mit dem RSA-Verfahren erlautert. Danach werden Abschatzungen behandelt, die unerlasslich sind, wenn man Objekte zahlen oder Laufzeiten wichtiger Algorithmen verstehen...

This book constitutes the proceedings of the 26th International Conference on Developments in Language Theory, DLT 2022, which was held in Tampa, FL, USA, during May, 2022. The conference took place in an hybrid format with both in-person and online participation.

The 21 full papers included in these proceedings were carefully reviewed and selected from 32 submissions. The DLT conference series provides a forum for presenting current developments in formal languages and automata.

Bei diskreten algebraischen Methoden handelt es sich um ein zukunftsweisendes Gebiet, dessen Grundlagen weiter an Bedeutung gewinnen werden. Die Grundidee des vorliegenden Lehrbuchs ist, wesentliche Elemente der diskreten Mathematik zu vermitteln, um die modernen Entwicklungen im Informationszeitalter kompetent mathematisch beurteilen zu konnen. Es beginnt mit einem allgemeinen Kapitel uber algebraische Strukturen, welches die Grundlage fur das gesamte Buch bereitstellt. Das folgende Kapitel vermittelt Grundkenntnisse in Kryptographie. Kapitel 3 uber zahlentheoretische Algorithmen ist...

The theory of traces employs techniques and tackles problems from quite diverse areas which include formal language theory, combinatorics, graph theory, algebra, logic, and the theory of concurrent systems. In all these areas the theory of traces has led to interesting problems and significant results. It has made an especially big impact in formal language theory and the theory of concurrent systems. In both these disciplines it is a well-recognized and dynamic research area. Within formal language theory it yields the theory of partially commutative monoids, and provides an important...

The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and...

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.

This volume presents the lecture notes from the authors' three summer courses offered during the program "Automorphisms of Free Groups: Geometry, Topology, and Dynamics," held at the Centre de Recerca Matematica (CRM) in Bellaterra, Spain.

The first two chapters present the basic tools needed, from formal language theory (regular and context-free languages, automata, rewriting systems, transducers, etc) and emphasize their connections to group theory, mostly relating to free and virtually-free groups. The material covered is sufficient to present full proofs of many of the...