Collecting information previously scattered throughout the vast literature, including the author s own research, Stochastic Relations: Foundations for Markov Transition Systems develops the theory of stochastic relations as a basis for Markov transition systems.

After an introduction to the basic mathematical tools from topology, measure theory, and categories, the book examines the central topics of congruences and morphisms, applies these to the monoidal structure, and defines bisimilarity and behavioral equivalence within this framework. The author views developments from the...

Coalgebraic logic is an important research topic in the areas of concurrency theory, semantics, transition systems and modal logics. It provides a general approach to modeling systems, allowing us to apply important results from coalgebras, universal algebra and category theory in novel ways. Stochastic systems provide important tools for systems modeling, and recent work shows that categorical reasoning may lead to new insights, previously not available in a purely probabilistic setting.

This book combines coalgebraic reasoning, stochastic systems and logics. It provides an insight...

Coalgebraic logic is an important research topic in the areas of concurrency theory, semantics, transition systems and modal logics. It provides a general approach to modeling systems, allowing us to apply important results from coalgebras, universal algebra and category theory in novel ways. Stochastic systems provide important tools for systems modeling, and recent work shows that categorical reasoning may lead to new insights, previously not available in a purely probabilistic setting.

This book combines coalgebraic reasoning, stochastic systems and logics. It provides an insight...

Haskell gilt als schwer zu lernende Sprache. Das mu nicht sein, wie dieses Buch zeigt. Der Verfasser nimmt die Leser mit auf eine Reise ins Land der funktionalen Programmierung. Er zeigt, da viele aus der objektorientierten Programmierung bekannten Algorithmen und Datenstrukturen knapp, durchsichtig und elegant formuliert werden konnen, ohne an Effizienz oder Verstandlichkeit zu verlieren. Ausfuhrliche Fallstudien begleiten die Einfuhrung in die Sprache wie Sehenswurdigkeiten. Hierzu gehoren die Diskussion der Vignere-Verschlusselung, die Huffman-Codierung, der Algorithmus von Kruskal und die...

Eine sanfte und zum Selbststudium gedachte Einfuhrung in die objektorientierte Programmierung und den Umgang mit C++. Der Aufbau der einzelnen Abschnitte folgt dem Schema, dass Syntax und Semantik der entsprechenden Sprachkonstrukte jeweils aus einem Beispiel entwickelt werden. An Hand zahlreicher Beispiele und Ubungsaufgaben konnen die vorgestellten Themen nachvollzogen und geubt werden.

This textbook addresses the mathematical description of sets, categories, topologies and measures, as part of the basis for advanced areas in theoretical computer science like semantics, programming languages, probabilistic process algebras, modal and dynamic logics and Markov transition systems. Using motivations, rigorous definitions, proofs and various examples, the author systematically introduces the Axiom of Choice, explains Banach-Mazur games and the Axiom of Determinacy, discusses the basic constructions of sets and the interplay of coalgebras and Kripke models for modal logics with...