Stochastic Relations: Foundations for Markov Transition Systems

ISBN-13: 9780367389116 / Angielski / Miękka / 2019 / 376 str.

Ernst-Erich Doberkat

Opis

This book 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, it examines congruences and morphisms. It applies these topics to the monoidal structure, and defines bisimilarity and behavioral equivalence within this framework. Developments from the general theory of coalgebras in the context of the subprobability functor are presented. The book also includes case studies of software architecture, the converse of a stochastic relation, and the average case analysis of two algorithms.

Spis treści

Introduction. A Gentle Tutorial to All Things Considered. Stochastic Relations as Monads. Eilenberg–Moore Algebras for Stochastic Relations. The Existence of Semi-Pullbacks. Congruences and Bisimulations. Interpreting Modal and Temporal Logics. Appendix. Bibliography. Index.

O autorze

Doberkat, Ernst-Erich