It is with great pleasure that we present to you this tutorial volume entitled Validation of Stochastic Systems.ItisoneoftheresultsoftheDutch-German- lateral cooperation project Validation of Stochastic Systems (VOSS), ?nanced by NWO and DFG (the Dutch and German science foundations, respectively). In the early days of 2002, the idea emerged to organize a seminar at Schloss Dagstuhl, not the usual Dagstuhl seminar with primarily invited participants, but a seminar aimed at young(er) people, and for which the organizers assign themes to be worked upon and presented on. Following an open call announced via the Internet in the spring of 2002, we received many applications for part- ipation. After a selection procedure, we decided to assign (mostly) teams of two researchers to work on speci?c topics, roughly divided into the following four theme areas: Modelling of Stochastic Systems, Model Checking of Stochastic Systems, Representing Large State Spaces, and Deductive Veri?cation of Stochastic Systems. These are the titles of the four parts of this volume. TheseminarwasheldinSchlossDagstuhlduringDecember8 11,2002aspart of the so-called GI/Research Seminar series. This series of seminars is ?nancially supported by theGesellschaft fur Informatik, the German Computer Society. At that point in time the papers had already undergone a ?rst review round. Each of the tutorial papers was presented in a one-hour session, and on the basis of the presentations we decided to bring together a selection of them into a book.

Inhalt
Modelling Stochastic Systems.- Probabilistic Automata: System Types, Parallel Composition and Comparison.- Tutte le Algebre Insieme: Concepts, Discussions and Relations of Stochastic Process Algebras with General Distributions.- An Overview of Probabilistic Process Algebras and Their Equivalences.- Model Checking of Stochastic Systems.- Verifying Qualitative Properties of Probabilistic Programs.- On Probabilistic Computation Tree Logic.- Model Checking for Probabilistic Timed Systems.- Representing Large State Spaces.- Serial Disk-Based Analysis of Large Stochastic Models.- Kronecker Based Matrix Representations for Large Markov Models.- Symbolic Representations and Analysis of Large Probabilistic Systems.- Probabilistic Methods in State Space Analysis.- Deductive Verification of Stochastic Systems.- Analysing Randomized Distributed Algorithms.- An Abstraction Framework for Mixed Non-deterministic and Probabilistic Systems.- The Verification of Probabilistic Lossy Channel Systems.